The mathematical development of set theory from Cantor to Cohen

Bulletin of Symbolic Logic

Volumn 2, Issue 1, 1996, Pages 1-71

  Kanamori, Akihiro ^a  

^a Boston University   (United States)

Author keywords

[No Author keywords available]

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EID: 0030494457     PISSN: 10798986     EISSN: None     Source Type: Journal    
DOI: 10.2307/421046     Document Type: Article

References (429)

1. [1965] John W. Addison, Jr., Leon Henkin, and Alfred Tarski (editors), The theory of models, Proceedings of the 1963 International Symposium at Berkeley, North-Holland, Amsterdam.
2. [1990] Donald J. Albers, Gerald L. Alexanderson, and Constance Reid (editors), More mathematical people, Harcourt Brace Jovanovich, Boston.
3. [1916] PAVEL S. ALEKSANDROV, Sur la puissance des ensembles mesurables B, Comptes Rendus Hebdomadaires des Séances de l'Académie des Sciences, Paris, vol. 162, pp. 323-325.
4. [1929] PAVEL S. ALEKSANDROV and PAUL URYSOHN, Mémoire sur les espaces topologiques compacts, Verhandelingen der Koninklijke Nederlandse Akademie van Wetenschappen Tweed Reeks, Afdeling Natuurkunde. vol. 14, pp. 1-96.
5. [1898] RENÉ BAIRE, Sur les fonctions discontinues qui se rattachent aux fonctions continues, Comptes Rendus Hebdomadaires des Séances de l'Académie des Sciences, Paris, vol. 129, pp. 1621-1623.
6. [1899] _, Sur les fonctions de variables réelles, Annali di Matematica Pura ed Applicara, vol. (3)3, pp. 1-123.
7. [1967] STEFAN BANACH, Oeuvres, vol. 1, Państwowe Wydawnictwo Naukowe, Warsaw, edited by Stanislaw Hartman and Edward Marczewski.
8. [1924] STEFAN BANACH and ALFRED TARSKI, Sur la décomposition des ensembles de points en parties respectivement congruentes, Fundamenta Mathematicae, vol. 6, pp. 244-277, reprinted in Banach [1967], pp. 118-148, and in Tarski [1986] vol. 1, pp. 121-154.
9. [1924] STEFAN BANACH and ALFRED TARSKI, Sur la décomposition des ensembles de points en parties respectivement congruentes, Fundamenta Mathematicae, vol. 6, pp. 244-277, reprinted in Banach [1967], pp. 118-148, and in Tarski [1986] vol. 1, pp. 121-154.
10. [1924] STEFAN BANACH and ALFRED TARSKI, Sur la décomposition des ensembles de points en parties respectivement congruentes, Fundamenta Mathematicae, vol. 6, pp. 244-277, reprinted in Banach [1967], pp. 118-148, and in Tarski [1986] vol. 1, pp. 121-154.
11. [1961] Yehoshua Bar-Hillel, E. I. J. Poznanski, Michael O. Rabin, and Abraham Robinson (editors), Essays on the foundations of mathematics, Magnes Press, Jerusalem.
12. [1995] TOMEK BARTOSZYŃSKI and HAIM JUDAH, Set theory. On the structure of the real line, A. K. Peters, Wellesley.
13. [1985] JOHN L. BELL. Boolean-valued models and independence proofs in set theory, second ed., Oxford Logic Guides #12, Oxford University Press, Oxford.
14. [1964] Paul Benacerraf and Hilary Putnam (editors), Philosophy of mathematics. Selected readings, Prentice Hall, Englewood Cliffs, N.J.
15. [1933] Paul Benacerraf and Hilary Putnam (editors), Philosophy of mathematics. Selected readings, second ed., Cambridge University Press, Cambridge.
16. [1883] IVAR BENDIXSON, Quelques théorèmes de la théorie des ensembles de points, Acta Mathematica, vol. 2, pp. 415-429.
17. [1937] PAUL BERNAYS, A system of axiomatic set theory. Part I, The Journal of Symbolic Logic, vol. 2, pp. 65-77.
18. [1976] _, A system of axiomatic set theory, Sets and Classes. On the work by Paul Bernays (Gert H. Müller, editor), North-Holland, Amsterdam, pp. 1-119, individually appeared as A system of axiomatic set theory in The Journal of Symbolic Logic, vol. 2 (1937), pp. 65-77; vol. 6 (1941), pp. 1-17; vol. 7 (1942), pp. 65-89, 133-145; vol. 8 (1943), pp. 89-106; vol. 13 (1948), pp. 65-79; and vol. 19 (1954), pp. 81-96.
19. [1976] _, A system of axiomatic set theory, Sets and Classes. On the work by Paul Bernays (Gert H. Müller, editor), North-Holland, Amsterdam, pp. 1-119, individually appeared as A system of axiomatic set theory in The Journal of Symbolic Logic, vol. 2 (1937), pp. 65-77; vol. 6 (1941), pp. 1-17; vol. 7 (1942), pp. 65-89, 133-145; vol. 8 (1943), pp. 89-106; vol. 13 (1948), pp. 65-79; and vol. 19 (1954), pp. 81-96.
20. [1976] _, A system of axiomatic set theory, Sets and Classes. On the work by Paul Bernays (Gert H. Müller, editor), North-Holland, Amsterdam, pp. 1-119, individually appeared as A system of axiomatic set theory in The Journal of Symbolic Logic, vol. 2 (1937), pp. 65-77; vol. 6 (1941), pp. 1-17; vol. 7 (1942), pp. 65-89, 133-145; vol. 8 (1943), pp. 89-106; vol. 13 (1948), pp. 65-79; and vol. 19 (1954), pp. 81-96.
21. [1976] _, A system of axiomatic set theory, Sets and Classes. On the work by Paul Bernays (Gert H. Müller, editor), North-Holland, Amsterdam, pp. 1-119, individually appeared as A system of axiomatic set theory in The Journal of Symbolic Logic, vol. 2 (1937), pp. 65-77; vol. 6 (1941), pp. 1-17; vol. 7 (1942), pp. 65-89, 133-145; vol. 8 (1943), pp. 89-106; vol. 13 (1948), pp. 65-79; and vol. 19 (1954), pp. 81-96.
22. [1976] _, A system of axiomatic set theory, Sets and Classes. On the work by Paul Bernays (Gert H. Müller, editor), North-Holland, Amsterdam, pp. 1-119, individually appeared as A system of axiomatic set theory in The Journal of Symbolic Logic, vol. 2 (1937), pp. 65-77; vol. 6 (1941), pp. 1-17; vol. 7 (1942), pp. 65-89, 133-145; vol. 8 (1943), pp. 89-106; vol. 13 (1948), pp. 65-79; and vol. 19 (1954), pp. 81-96.
23. [1976] _, A system of axiomatic set theory, Sets and Classes. On the work by Paul Bernays (Gert H. Müller, editor), North-Holland, Amsterdam, pp. 1-119, individually appeared as A system of axiomatic set theory in The Journal of Symbolic Logic, vol. 2 (1937), pp. 65-77; vol. 6 (1941), pp. 1-17; vol. 7 (1942), pp. 65-89, 133-145; vol. 8 (1943), pp. 89-106; vol. 13 (1948), pp. 65-79; and vol. 19 (1954), pp. 81-96.
24. [1976] _, A system of axiomatic set theory, Sets and Classes. On the work by Paul Bernays (Gert H. Müller, editor), North-Holland, Amsterdam, pp. 1-119, individually appeared as A system of axiomatic set theory in The Journal of Symbolic Logic, vol. 2 (1937), pp. 65-77; vol. 6 (1941), pp. 1-17; vol. 7 (1942), pp. 65-89, 133-145; vol. 8 (1943), pp. 89-106; vol. 13 (1948), pp. 65-79; and vol. 19 (1954), pp. 81-96.
25. [1908] FELIX BERNSTEIN, Zur theorie der trigonometrischen Reihen, Berichte über die Verhandlungen der Königlich Sächsischen Gesellschaft der Wissenschaften zu Leipzig, Mathematische-Physische Klasse, vol. 60, pp. 325-338.
26. [1984] ANDREAS R. BLASS, Existence of bases implies the Axiom of Choice, Axiomatic set theory (James E. Baumgartner, Donald A. Martin, and Saharon Shelah, editors), Contemporary Mathematics, vol. 31, American Mathematical Society, Providence, pp. 31-33.
27. [1971] GEORGE S. BOOLOS, The iterative concept of set, Journal of Philosophy, vol. 68, pp. 215-231, reprinted in Benacerraf-Putnam [1983], pp. 486-502.
28. [1971] GEORGE S. BOOLOS, The iterative concept of set, Journal of Philosophy, vol. 68, pp. 215-231, reprinted in Benacerraf-Putnam [1983], pp. 486-502.
29. [1898] EMILE BOREL, Leçons sur la théorie des fonctions, Gauthier-Villars, Paris.
30. [1919] _, Sur la classification des ensembles de mesure nulle, Bulletin de la Société Mathématique de France, vol. 47, pp. 97-125.
31. [1911] LUITZEN E. J. BROUWER, Beweis der Invariaz: der Dimensionenzahl, Mathematische Annalen, vol. 70, pp. 161-165, reprinted in [1976] below, pp. 430-434.
32. [1911] LUITZEN E. J. BROUWER, Beweis der Invariaz: der Dimensionenzahl, Mathematische Annalen, vol. 70, pp. 161-165, reprinted in [1976] below, pp. 430-434.
33. [1976] _, Collected works, vol. 2, North-Holland, Amsterdam, edited by Hans Freudenthal.
34. [1897] CESARE BURALI-FORTI, Una questione sui numeri transfini, Rendiconti del Circolo Matematico di Palermo, vol. 11, pp. 154-164, translated in van Heijenoort [1967], pp. 104-111.
35. [1897] CESARE BURALI-FORTI, Una questione sui numeri transfini, Rendiconti del Circolo Matematico di Palermo, vol. 11, pp. 154-164, translated in van Heijenoort [1967], pp. 104-111.
36. [1872] GEORG CANTOR, Über die Ausdehnung eines Satzes aus der Theorie der trignometrischen Reihen, Mathematische Annalen, vol. 5, pp. 123-132, reprinted in [1932] below, pp. 92-102.
37. [1872] GEORG CANTOR, Über die Ausdehnung eines Satzes aus der Theorie der trignometrischen Reihen, Mathematische Annalen, vol. 5, pp. 123-132, reprinted in [1932] below, pp. 92-102.
38. [1874] _, Über eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen, Journal für die reine und angewandte Mathematik (Crelle's Journal), vol. 77, pp. 258-262, reprinted in [1932] below, pp. 115-118.
39. _, Über eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen, Journal für die reine und angewandte Mathematik (Crelle's Journal), vol. 77, pp. 258-262, reprinted in [1932] below, pp. 115-118.
40. [1878] _, Ein Beitrag zur Mannigfaltigkeitslehre, Journal für die reine und angewandte Mathematik (Crelle's Journal), vol. 84, pp. 242-258, reprinted in [1932] below, pp. 119-133.
41. [1878] _, Ein Beitrag zur Mannigfaltigkeitslehre, Journal für die reine und angewandte Mathematik (Crelle's Journal), vol. 84, pp. 242-258, reprinted in [1932] below, pp. 119-133.
42. [1879] _, Über einen Satz aus der Theorie der stetigen Mannigfaltigkeiten, Nachrichten von der Königlichen Gesellschaft der Wissenschaften und der Georg-Augusts-Universität zu Göttingen, pp. 127-135, reprinted in [1932] below, pp. 134-138.
43. [1879] _, Über einen Satz aus der Theorie der stetigen Mannigfaltigkeiten, Nachrichten von der Königlichen Gesellschaft der Wissenschaften und der Georg-Augusts-Universität zu Göttingen, pp. 127-135, reprinted in [1932] below, pp. 134-138.
44. [1880] _, Über unendliche, lineare punktmannigfaltigkeiten. II, Mathematische Annalen, vol. 17, pp. 355-358, reprinted in [1932]below, pp. 145-148, but excluding the referenced remark.
45. [1880] _, Über unendliche, lineare punktmannigfaltigkeiten. II, Mathematische Annalen, vol. 17, pp. 355-358, reprinted in [1932]below, pp. 145-148, but excluding the referenced remark.
46. [1883] _, Über unendliche, lineare punktmannigfaltigkeiten. V, Mathematische Annalen, vol. 21, pp. 545-591, published separately as Grundlagen einer allgemeinen Mannigfaltigkeitslehre. Ein mathematisch-philosophischer Versuch in der Lehre des Unendlichen, B. G. Teubner, Leipzig, 1883; reprinted in [1932] below, pp. 165-209.
47. [1883] _, Über unendliche, lineare punktmannigfaltigkeiten. V, Mathematische Annalen, vol. 21, pp. 545-591, published separately as Grundlagen einer allgemeinen Mannigfaltigkeitslehre. Ein mathematisch-philosophischer Versuch in der Lehre des Unendlichen, B. G. Teubner, Leipzig, 1883; reprinted in [1932] below, pp. 165-209.
48. [1883] _, Über unendliche, lineare punktmannigfaltigkeiten. V, Mathematische Annalen, vol. 21, pp. 545-591, published separately as Grundlagen einer allgemeinen Mannigfaltigkeitslehre. Ein mathematisch-philosophischer Versuch in der Lehre des Unendlichen, B. G. Teubner, Leipzig, 1883; reprinted in [1932] below, pp. 165-209.
49. [1884] _, Über unendliche, lineare punktmannigfaltigkeiten. VI, Mathematische Annalen, vol. 23, pp. 453-488, reprinted in [1932] below, pp. 210-246.
50. [1884] _, Über unendliche, lineare punktmannigfaltigkeiten. VI, Mathematische Annalen, vol. 23, pp. 453-488, reprinted in [1932] below, pp. 210-246.
51. [1884a] _, De la puissance des ensembles parfaits de points, Acta Mathematica, vol. 4, pp. 381-392, reprinted in [1932] below, pp. 252-260.
52. [1884a] _, De la puissance des ensembles parfaits de points, Acta Mathematica, vol. 4, pp. 381-392, reprinted in [1932] below, pp. 252-260.
53. [1887] _, Mitteilungen zur Lehre vom Transfiniten, Zeitschrift für Philosophie und philosophische Kritik, vol. 91, pp. 81-125, 252-270, reprinted in [1932] below, pp. 378-439.
54. [1887] _, Mitteilungen zur Lehre vom Transfiniten, Zeitschrift für Philosophie und philosophische Kritik, vol. 91, pp. 81-125, 252-270, reprinted in [1932] below, pp. 378-439.
55. [1891] _, Über eine elementare Frage der Mannigfaltigkeitslehre, Jahresbericht der Deutschen Mathematiker-Vereinigung, vol. I, pp. 75-78, reprinted in [1932] below, pp. 278-280.
56. [1891] _, Über eine elementare Frage der Mannigfaltigkeitslehre, Jahresbericht der Deutschen Mathematiker-Vereinigung, vol. I, pp. 75-78, reprinted in [1932] below, pp. 278-280.
57. [1895] _, Beiträge zur Begründung der transfiniten Mengenlehre. I, Mathematische Annalen, vol. 46, pp. 481-512, translated in [1915] below; reprinted in [1932] below, pp. 282-311.
58. [1895] _, Beiträge zur Begründung der transfiniten Mengenlehre. I, Mathematische Annalen, vol. 46, pp. 481-512, translated in [1915] below; reprinted in [1932] below, pp. 282-311.
59. [1897] _, Beiträge zur Begründung der transfiniten Mengenlehre. II, Mathematische Annalen, vol. 49, pp. 207-246, translated in [1915] below; reprinted in [1932] below, pp. 312-351.
60. [1897] _, Beiträge zur Begründung der transfiniten Mengenlehre. II, Mathematische Annalen, vol. 49, pp. 207-246, translated in [1915] below; reprinted in [1932] below, pp. 312-351.
61. [1915] _, Contributions to the founding of the theory of transfinite numbers, Open Court, Chicago, translation of [1895] and [1897] above with introduction and notes by Philip E. B. Jourdain; reprinted Dover, New York, 1965.
62. [1932] _, Gesammelte Abhandlungen mathematischen und philosophischen Inhalts, Julius Springer, Berlin, edited by Ernst Zermelo, reprinted Springer-Verlag, Berlin, 1980.
63. [1962] JEAN CAVAILLÈS, Philosophie mathématique, Hermann, Paris, includes French translation of Noether-Cavaillès [1937].
64. [1990] CHEN-CHUNG CHANG and H. JEROME KEISLER, Model theory, third ed., North-Holland, Amsterdam.
65. [1979] J. ALBERTO COFFA, The humble origins of Russell's paradox, Russell, vol. 33-34, pp. 31-37.
66. [1963] PAUL J. COHEN, The independence of the Continuum Hypothesis. I, Proceedings of the National Academy of Sciences U.S.A., vol. 50, pp. 1143-1148.
67. [1964] _, The independence of the Continuum Hypothesis. II, Proceedings of the National Academy of Sciences U.S.A., vol. 51, pp. 105-110.
68. [1965] _, Independence results in set theory, in Addison-Henkin-Tarski [1965], pp. 39-54.
69. [1979] JOSEPH W. DAUBEN, Georg Cantor. His mathematics and philosophy of the infinite, Harvard University Press, Cambridge, paperback edition 1990.
70. [1871] RICHARD DEDEKIND, Supplement to the second edition of Dirichlet's Vorlesungen über Zahlentheorie, F. Vieweg, Braunschweig, reprinted in [1932] below, vol. 3, pp. 399-407.
71. [1871] RICHARD DEDEKIND, Supplement to the second edition of Dirichlet's Vorlesungen über Zahlentheorie, F. Vieweg, Braunschweig, reprinted in [1932] below, vol. 3, pp. 399-407.
72. [1872] _, Stetigkeit und irrationale Zahlen, F. Vieweg, Braunschweig, fifth. 1927 edition reprinted in [1932] below, vol. 3, pp. 315-334; translated in [1963] below, pp. 1-27.
73. [1872] _, Stetigkeit und irrationale Zahlen, F. Vieweg, Braunschweig, fifth. 1927 edition reprinted in [1932] below, vol. 3, pp. 315-334; translated in [1963] below, pp. 1-27.
74. [1872] _, Stetigkeit und irrationale Zahlen, F. Vieweg, Braunschweig, fifth. 1927 edition reprinted in [1932] below, vol. 3, pp. 315-334; translated in [1963] below, pp. 1-27.
75. [1888] _, Was sind und was sollen die Zahlen?, F. Vieweg, Braunschweig, sixth, 1930 edition reprinted in [1932] below, vol. 3, pp. 335-390; second, 1893 edition translated in [1963] below, pp. 29-115.
76. [1888] _, Was sind und was sollen die Zahlen?, F. Vieweg, Braunschweig, sixth, 1930 edition reprinted in [1932] below, vol. 3, pp. 335-390; second, 1893 edition translated in [1963] below, pp. 29-115.
77. [1888] _, Was sind und was sollen die Zahlen?, F. Vieweg, Braunschweig, sixth, 1930 edition reprinted in [1932] below, vol. 3, pp. 335-390; second, 1893 edition translated in [1963] below, pp. 29-115.
78. [1900] _, Über die von drei Moduln erzeugte Dualgruppe, Mathematische Annalen, vol. 53, pp. 371-403, reprinted in [1932] below, vol. 2, pp. 236-271.
79. [1900] _, Über die von drei Moduln erzeugte Dualgruppe, Mathematische Annalen, vol. 53, pp. 371-403, reprinted in [1932] below, vol. 2, pp. 236-271.
80. [1932] _, Gesammelte mathematische Werke, F. Vieweg, Baunschweig, edited by Robert Fricke, Emmy Noether and Öystein Ore, reprinted Chelsea, New York, 1969.
81. [1963] _, Essays on the theory of numbers, Dover, New York, translation by Wooster W. Bemun (reprint of original edition, Open Court, Chicago, 1901).
82. [1979] BURTON DREBEN and WARREN D. GOLDFARB, The decision problem: Solvable classes of quantificational formulas, Addison-Wesley, Reading.
83. [1869] PAUL DU BOIS-REYMOND, Bemerkungen über die verschidenen Werthe, welche eine Function zweier reellen Variabein erhält, wenn man diese Variabeln entweder nach einander oder gewissen Beziehungen gemäss gleichzeitig verschwinden lässt, Journal für die reine und angewandte Mathematik (Crelle's Journal), vol. 70, pp. 10-45.
84. [1875] _, Über asymptotische Werthe, infinitäre Approximationen und infinitäre Auflösung von Gleichungen, Mathematische Annalen, vol. 8, pp. 363-114.
85. [1976] PIERRE DUGAC, Richard Dedekind et les fondements des mathématiques, Collection des travaux de l'Académie Internationale d'Histoire des Sciences #24, J. Vrin, Paris.
86. [1964] WILLIAM B. EASTON, Powers of regular cardinals, Ph.D. thesis, Princeton University, abstracted as: Proper classes of generic sets, Notices of the American Mathematical Society, vol. 11 (1964), p. 205; published in abridged form as [1970] below.
87. [1970] _, Powers of regular cardinals, Annals of Mathematical Logic, vol. 1, pp. 139-178.
88. [1956] ANDRZEJ EHRENFEUCHT and ANDRZEJ M. MOSTOWSKI, Models of axiomatic theories admitting automorphisms, Fundamenta Mathematicae, vol. 43, pp. 50-68, reprinted in Mostowski [1979], pp. 494-512.
89. [1956] ANDRZEJ EHRENFEUCHT and ANDRZEJ M. MOSTOWSKI, Models of axiomatic theories admitting automorphisms, Fundamenta Mathematicae, vol. 43, pp. 50-68, reprinted in Mostowski [1979], pp. 494-512.
90. [1962] PAUL ERDÖS and ANDRÁS HAJNAL, Some remarks concerning our paper "On the structure of set mappings", Acta Mathematica Academiae Scientiarum Hungaricae, vol. 13, pp. 223-226.
91. [1984] PAUL ERDÖS, ANDRÁS HAJNAL, ATTILA MÁTÉ, and RICHARD RADO, Combinatorial set theory: Partition relations for cardinals, North-Holland, Amsterdam.
92. [1965] PAUL ERDÖS, ANDRÁS HAJNAL, and RICHARD RADO, Partition relations for cardinal numbers, Acta Mathematica Academiae Scientiarum Hungaricae, vol. 16, pp. 93-196.
93. [1956] PAUL ERDÖS and RICHARD RADO, A partition calculus in set theory, Bulletin of the American Mathematical Society, vol. 62, pp. 427-489, reprinted in Gessel-Rota [1987], pp. 179-241.
94. [1956] PAUL ERDÖS and RICHARD RADO, A partition calculus in set theory, Bulletin of the American Mathematical Society, vol. 62, pp. 427-489, reprinted in Gessel-Rota [1987], pp. 179-241.
95. [1943] PAUL ERDÖS and ALFRED TARSKI, On families of mutually exclusive sets, Annals of Mathematics, vol. 44, pp. 315-329, reprinted in Tarski [1986], vol. 2, pp. 591-605.
96. [1943] PAUL ERDÖS and ALFRED TARSKI, On families of mutually exclusive sets, Annals of Mathematics, vol. 44, pp. 315-329, reprinted in Tarski [1986], vol. 2, pp. 591-605.
97. [1961] _, On some problems involving inaccessible cardinals, in Bar-Hillel-Poznanski-Rabin-Robinson [1961], pp. 50-82; reprinted in Tarski [1986], vol. 4, pp. 79-111.
98. [1961] _, On some problems involving inaccessible cardinals, in Bar-Hillel-Poznanski-Rabin-Robinson [1961], pp. 50-82; reprinted in Tarski [1986], vol. 4, pp. 79-111.
99. [1963] SOLOMON FEFERMAN and AZRIEL LEVY, Independence results in set theory by Cohen's method. II (abstract), Notices of the American Mathematical Society, vol. 10, p. 593.
100. [1971] ULRICH FELGNER, Models of ZF-set theory, Lecture Notes in Mathematics #223, Springer-Verlag, Berlin.
101. [1995] JOSÉ FERREIRÓS, "What fermented in me for years": Cantor's discovery of transfinite numbers, Historia Mathematica, vol. 22, pp. 33-42.
102. [1956] GÉZA FODOR, Eine Bemerking zur Theorie der regressiven Funktionen, Acta Scientiarum Mathematicarum, Szeged, vol. 17, pp. 139-142.
103. [1921] ABRAHAM A. FRAENKEL, Über die Zermelosche Begründung der Mengenlehre (abstract), Jahresbericht der Deutschen Mathematiker-Vereinigung, vol. 30, no. II, pp. 97-98.
104. [1922] _, Zu den Grundlagen der Cantor-Zermeloschen Mengenlehre, Mathematische Annalen, vol. 86, pp. 230-237.
105. [1922a] _, Über den Begriff 'definit' und die Unabhängigkeit des Auswahlaxioms, Sitzungsberichte der Preussischen Akademie der Wissenschaften, Physikalisch-mathematische Klasse, pp. 253-257, translated in van Heijenoort [1967], pp. 284-289.
106. [1922a] _, Über den Begriff 'definit' und die Unabhängigkeit des Auswahlaxioms, Sitzungsberichte der Preussischen Akademie der Wissenschaften, Physikalisch-mathematische Klasse, pp. 253-257, translated in van Heijenoort [1967], pp. 284-289.
107. [1930] _, Georg Cantor, Jahresbericht der Deutschen Mathematiker-Vereinigung, vol. 39, pp. 189-266, published separately as Georg Cantor, B. G. Teubner, Leipzig, 1930; published in abridged form in Cantor [1932], pp. 452-483.
108. [1930] _, Georg Cantor, Jahresbericht der Deutschen Mathematiker-Vereinigung, vol. 39, pp. 189-266, published separately as Georg Cantor, B. G. Teubner, Leipzig, 1930; published in abridged form in Cantor [1932], pp. 452-483.
109. [1953] _, Abstract set theory, North-Holland, Amsterdam.
110. [1879] GOTTLOB FREGE, Begriffsschrift, eine der arithmetischen nachg̈ebildete Formelsprache des reinen Denkens, Nebert, Halle, reprinted Hildesheim, Olms, 1964; translated in van Heijenoort [1967], pp. 1-82.
111. [1879] GOTTLOB FREGE, Begriffsschrift, eine der arithmetischen nachg̈ebildete Formelsprache des reinen Denkens, Nebert, Halle, reprinted Hildesheim, Olms, 1964; translated in van Heijenoort [1967], pp. 1-82.
112. [1884] _, Die Grundlagen der Arithmetik, eine logisch-mathematische Untersuchung über den Begriff der Zahl, Wilhelm Köbner, Breslau, translated with German text by John L. Austin, as The foundations of arithmetic, a logico-mathematical enquiry into the concept of number, Oxford, Blackwell, 1950; later editions without German text, Harper, New York.
113. [1884] _, Die Grundlagen der Arithmetik, eine logisch-mathematische Untersuchung über den Begriff der Zahl, Wilhelm Köbner, Breslau, translated with German text by John L. Austin, as The foundations of arithmetic, a logico-mathematical enquiry into the concept of number, Oxford, Blackwell, 1950; later editions without German text, Harper, New York.
114. [1891] _, Function und Begriff, Hermann Pohle, Jena, translated in [1952] below, pp. 21-41.
115. [1891] _, Function und Begriff, Hermann Pohle, Jena, translated in [1952] below, pp. 21-41.
116. [1893] _, Grundgesetze der Arithmetik, Begriffsschriftlich abgeleitet, vol. 1, Hermann Pohle, Jena, reprinted Hildesheim, Olms, 1962; partially translated in [1964] below.
117. [1893] _, Grundgesetze der Arithmetik, Begriffsschriftlich abgeleitet, vol. 1, Hermann Pohle, Jena, reprinted Hildesheim, Olms, 1962; partially translated in [1964] below.
118. [1895] _, Kritische Beleuchtung einiger Punkte in E. Schröders Vorlesungen über die Algebra der Logik, Archiv für systematische Philosophie, vol. 1, pp. 433-456, translated in [1952] below, pp. 86-106.
119. [1895] _, Kritische Beleuchtung einiger Punkte in E. Schröders Vorlesungen über die Algebra der Logik, Archiv für systematische Philosophie, vol. 1, pp. 433-456, translated in [1952] below, pp. 86-106.
120. [1903] _, vol. 2 of [1893]; reprinted Hildesheim, Olms, 1962.
121. [1952] _, Translations from the philosophical writings of Gottlob Frege, Blackwell, Oxford, translated and edited by Peter Geach and Max Black, second, revised edition 1960; latest edition, Rowland & Littlewood, Totowa, 1980.
122. [1964] _, The basic laws of arithmetic. Exposition of the system, California Press, Berkeley, California, edited by Montgomery Furth.
123. [1992] ALEJANDRO GARCIADIEGO, Bertrand Russell and the origins of the set-theoretic "paradoxes", Birkhäuser, Boston.
124. [1936] GERHARD GENTZEN, Die Widerspruchsfreiheit der reinen Zahlentheorie, Mathematicshe Annalen, vol. 112, pp. 493-565, translated in [1969] below, pp. 132-213.
125. [1936] GERHARD GENTZEN, Die Widerspruchsfreiheit der reinen Zahlentheorie, Mathematicshe Annalen, vol. 112, pp. 493-565, translated in [1969] below, pp. 132-213.
126. [1943] _, Beweisbarkeit und Unbeweisbarkeit von Anfangsfällen der transfiniten Induktion in der reinen Zahlentheorie, Mathematicshe Annalen, vol. 119, pp. 140-161, translated in [1969] below, pp. 287-308.
127. [1943] _, Beweisbarkeit und Unbeweisbarkeit von Anfangsfällen der transfiniten Induktion in der reinen Zahlentheorie, Mathematicshe Annalen, vol. 119, pp. 140-161, translated in [1969] below, pp. 287-308.
128. [1969] _, The collected papers of Gerhard Gentzen, North-Holland, Amsterdam, edited by M. E. Szabo.
129. [1987] Ira Gessel and Gian-Carlo Rota (editors), Classic papers in combinatorics, Birkhäuser, Boston.
130. [1992] MOTI GITIK and MENACHEM MAGIDOR, The singular cardinals hypothesis revisited, Set theory of the Continuum (Haim Judah, Winfried Just, and W. Hugh Woodin, editors), Mathematical Sciences Research Institute Publication #26, Springer-Verlag, Berlin, pp. 243-279.
131. [1930] KURT F. GÖDEL, Die Vollständigkeit der Axiome des logischen Funktionenkalküls, Monatshefte für Mathematik und Physik, vol. 37, pp. 349-360, reprinted and translated in [1986] below, pp. 102-123.
132. [1930] KURT F. GÖDEL, Die Vollständigkeit der Axiome des logischen Funktionenkalküls, Monatshefte für Mathematik und Physik, vol. 37, pp. 349-360, reprinted and translated in [1986] below, pp. 102-123.
133. [1931] _, Über formal unentscheidbare Sät:e der Principia Mathematica und verwandter Systeme I, Monatshefte für Mathematik und Physik, vol. 38, pp. 173-198, reprinted and translated with minor emendations by the author in [1986] below, pp. 144-195.
134. [1931] _, Über formal unentscheidbare Sät:e der Principia Mathematica und verwandter Systeme I, Monatshefte für Mathematik und Physik, vol. 38, pp. 173-198, reprinted and translated with minor emendations by the author in [1986] below, pp. 144-195.
135. [1938] _, The consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis, Proceedings of the National Academy of Sciences U.S.A., vol. 24, pp. 556-557, reprinted in [1990] below, pp. 26-27.
136. [1938] _, The consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis, Proceedings of the National Academy of Sciences U.S.A., vol. 24, pp. 556-557, reprinted in [1990] below, pp. 26-27.
137. [1939] _, Consistency-proof for the Generalized Continuum-Hypothesis, Proceedings of the National Academy of Sciences U.S.A., vol. 25, pp. 220-224, reprinted in [1990] below, pp. 28-32.
138. [1939] _, Consistency-proof for the Generalized Continuum-Hypothesis, Proceedings of the National Academy of Sciences U.S.A., vol. 25, pp. 220-224, reprinted in [1990] below, pp. 28-32.
139. [1940] _, The consistency of the Axiom of Choice and of the Generalized Continuum Hypothesis with the axioms of set theory, Annals of Mathematics Studies #3, Princeton University Press, Princeton, reprinted in [1990] below, pp. 33-101.
140. [1940] _, The consistency of the Axiom of Choice and of the Generalized Continuum Hypothesis with the axioms of set theory, Annals of Mathematics Studies #3, Princeton University Press, Princeton, reprinted in [1990] below, pp. 33-101.
141. [1947] _, What is Cantor's Continuum problem?, American Mathematical Monthly, vol. 54, pp. 515-525, Errata, vol. 55 (1948), p. 151; reprinted in [1990] below, pp. 176-187; revised and expanded version in Benacerraf-Putnam [1964], pp. 258-273; this version reprinted with minor emendations by the author in [1990] below, pp. 254-270.
142. _, What is Cantor's Continuum problem?, American Mathematical Monthly, vol. 54, pp. 515-525, Errata, vol. 55 (1948), p. 151; reprinted in [1990] below, pp. 176-187; revised and expanded version in Benacerraf-Putnam [1964], pp. 258-273; this version reprinted with minor emendations by the author in [1990] below, pp. 254-270.
143. _, What is Cantor's Continuum problem?, American Mathematical Monthly, vol. 54, pp. 515-525, Errata, vol. 55 (1948), p. 151; reprinted in [1990] below, pp. 176-187; revised and expanded version in Benacerraf-Putnam [1964], pp. 258-273; this version reprinted with minor emendations by the author in [1990] below, pp. 254-270.
144. _, What is Cantor's Continuum problem?, American Mathematical Monthly, vol. 54, pp. 515-525, Errata, vol. 55 (1948), p. 151; reprinted in [1990] below, pp. 176-187; revised and expanded version in Benacerraf-Putnam [1964], pp. 258-273; this version reprinted with minor emendations by the author in [1990] below, pp. 254-270.
145. [1986] _, Collected works, vol. 1, Oxford University Press, New York, edited by Solomon Feferman and others.
146. [1990] _, Collected works, vol. 2, Oxford University Press, New York, edited by Solomon Feferman and others.
147. [1979] WARREN D. GOLDFARB, Logic in the twenties: the nature of the quantifier, The Journal of Symbolic Logic, vol. 44, pp. 351-368.
148. [1990] RONALD L. GRAHAM, BRUCE L. ROTHSCHILD, and JOEL H. SPENCER, Ramsey theory, second ed., Wiley & Sons, New York.
149. [1974] IVOR GRATTAN-GUINNESS, The rediscovery of the Cantor-Dedekind correspondence, Jahresbericht der Deutschen Mathematiker-Vereinigung, vol. 76, pp. 104-139.
150. [1978] _, How Bertrand Russell discovered his paradox, Historia Mathematica, vol. 5, pp. 127-137.
151. [1994] ROBERT GRAY, Georg Cantor and transcendental numbers, American Mathematical Monthly, vol. 101, pp. 819-832.
152. [1971] PETR HÁJEK, Sets, semisets, models, in Scott [1971], pp. 67-81.
153. [1956] ANDRÁS HAJNAL, On a consistency theorem connected with the generalized continuum problem, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, vol. 2, pp. 131-136.
154. [1961] _, On a consistency theorem connected with the generalized continuum problem, Acta Mathematica Academiae Scientiarum Hungaricae, vol. 12, pp. 321-376.
155. [1984] MICHAEL HALLETT, Cantorian set theory and limitation of size, Logic Guides #10, Clarendon Press, Oxford.
156. [1961] JAMES D. HALPERN, The independence of the Axiom of Choice from the boolean prime ideal theorem (abstract), Notices of the American Mathematical Society, vol. 8, pp. 279-280.
157. [1964] _, The independence of the Axiom of Choice from the boolean prime ideal theorem, Fundamenta Mathematicae, vol. 55, pp. 57-66.
158. [1966] JAMES D. HALPERN and HANS LÄUCHLI, A partition theorem, Transactions of the American Mathematical Society, vol. 124, pp. 360-367.
159. [1971] JAMES D. HALPERN and AZRIEL LEVY, The Boolean prime ideal theorem does not imply the axiom of choice, in Scott [1971], pp. 83-134.
160. [1905] GEORG HAMEL, Eine Basis aller Zahlen und die unstetigen Lösungen der Funktionalgleichung: f (x + y) = f (x) + f (y), Mathematische Annalen, vol. 60, pp. 459-462.
161. [1964] WILLIAM P. HANF, Incompactness in languages with infinitely long expressions, Fundamenta Mathematicae, vol. 53, pp. 309-324.
162. [1915] FRIEDRICH HARTOGS, Über das Problem der Wohlordnung, Mathematische Annalen, vol. 76, pp. 436-443.
163. [1908] FELIX HAUSDORFF, Grundzüge einer Theorie der geordneten Mengen, Mathematische Annalen, vol. 65, pp. 435-505.
164. [1914] _, Grundzüge der Mengenlehre, de Gruyter, Leipzig, reprinted Chelsea, New York, 1965.
165. [1914a] _, Bemerkung über den Inhalt von Punktmengen, Mathematische Annalen, vol. 75, pp. 428-433.
166. [1916] _, Die Mächtigkeit der Borelschen Mengen, Mathematische Annalen, vol. 77, pp. 430-437.
167. [1932] _, Zur Theorie der linearen metrischen Räume, Journal für die reine und angewandte Mathematik (Crelle's Journal), vol. 167, pp. 294-311.
168. [1937] _, Mengenlehre, third, revised edition of [1914]; translated by John R. Auman as Set Theory, Chelsea, New York, 1962.
169. [1937] _, Mengenlehre, third, revised edition of [1914]; translated by John R. Auman as Set Theory, Chelsea, New York, 1962.
170. [1975] THOMAS W. HAWKINS, Lebesgue's theory of integration. Its origins and development, second ed., Chelsea, New York.
171. [1949] LEON HENKIN, The completeness of the first-order functional calculus, The Journal of Symbolic Logic, vol. 14, pp. 159-166.
172. [1906] GERHARD HESSENBERG, Grundbegriffe der mengenlehre, Vandenhoeck & Ruprecht, Göttingen, reprinted from Abhandlungen der Fries'schen Schule, Neue Folge, vol. 1 (1906), pp. 479-706.
173. [1906] GERHARD HESSENBERG, Grundbegriffe der mengenlehre, Vandenhoeck & Ruprecht, Göttingen, reprinted from Abhandlungen der Fries'schen Schule, Neue Folge, vol. 1 (1906), pp. 479-706.
174. [1900] DAVID HILBERT, Mathematische Probleme, Vortrag, gehalten auf dem internationalem Mathematiker-Kongress zu Paris. 1900. Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen, pp. 253-297, translated in the Bulletin of the American Mathematical Society, vol. 8 (1902), pp. 437-479.
175. [1900] DAVID HILBERT, Mathematische Probleme, Vortrag, gehalten auf dem internationalem Mathematiker-Kongress zu Paris. 1900. Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen, pp. 253-297, translated in the Bulletin of the American Mathematical Society, vol. 8 (1902), pp. 437-479.
176. [1926] _, Über dan Unendliche, Mathematische Annalen, vol. 95, pp. 161-190, translated in van Heijenoort [1967], pp. 367-392; partially translated in Benacerraf-Putnam [1983], pp. 183-201.
177. [1926] _, Über dan Unendliche, Mathematische Annalen, vol. 95, pp. 161-190, translated in van Heijenoort [1967], pp. 367-392; partially translated in Benacerraf-Putnam [1983], pp. 183-201.
178. [1926] _, Über dan Unendliche, Mathematische Annalen, vol. 95, pp. 161-190, translated in van Heijenoort [1967], pp. 367-392; partially translated in Benacerraf-Putnam [1983], pp. 183-201.
179. [1928] DAVID HILBERT and WILHELM ACKERMANN, Grundzüge der theoretischen Logik, Julius Springer, Berlin, second edition, 1938; third edition, 1949; second edition was translated by Lewis M. Hammond, George G. Leckie and F. Steinhardt as Principles of mathematical logic, Chelsea, New York, 1950.
180. [1928] DAVID HILBERT and WILHELM ACKERMANN, Grundzüge der theoretischen Logik, Julius Springer, Berlin, second edition, 1938; third edition, 1949; second edition was translated by Lewis M. Hammond, George G. Leckie and F. Steinhardt as Principles of mathematical logic, Chelsea, New York, 1950.
181. [1993] WILFRID HODGES, Model theory, Encyclopedia of Mathematics and its Applications, vol. 42, Cambridge University Press, Cambridge.
182. [1973] THOMAS J. JECH, The Axiom of Choice, North-Holland, Amsterdam.
183. [1978] _, Set theory, Academic Press, New York.
184. [1995] _, Singular cardinals and the PCF theory, this BULLETIN, vol. 1, pp. 408-424.
185. [1966] THOMAS J. JECH and ANTONIN SOCHOR, Applications of the θ-model, Bulletin de l'Académie Polonaise des Sciences, Série des Sciences Mathématiques, Astronomiques et Physiques, vol. 14, pp. 351-355.
186. [1972] RONALD B. JENSEN, The fine structure of the constructible hierarchy, Annals of Mathematical Logic, vol. 4, pp. 229-308.
187. [1968] MARK KAC and STANISLAW M. ULAM, Mathematics and logic, Praeger, New York.
188. [1994] AKIHIRO KANAMORI, The higher infinite, Springer-Verlag, Berlin.
189. [1995] _, The emergence of descriptive set theory, From Dedekind to Gödel. Essays on the development of the foundations of mathematics (Jaakko Hintikka, editor), Synthese Library No. 251, Kluwer Publishing, Dordrecht, pp. 241-262.
190. [∞] _, The higher infinite II, Springer-Verlag, Berlin, to appear.
191. [1987] ALEXANDER S. KECHRIS and ALAIN LOUVEAU, Descriptive set theory and the structure of sets of uniqueness, London Mathematical Society Lecture Note Series #128, Cambridge University Press, Cambridge.
192. [1962] H. JEROME KEISLER, Some applications of the theory of models to act theory, Logic, methodology and philosophy of science (Ernest Nagel, Patrick Suppes, and Alfred Tarski, editors), Stanford University Press, Stanford, Proceedings of the 1960 [and first] International Congress (Stanford, California), pp. 80-86.
193. [1962a] _, The equivalence of certain problems in set theory with problems in the theory of models (abstract), Notices of the American Mathematical Society, vol. 9, pp. 339-340.
194. [1964] H. JEROME KEISLER and ALFRED TARSKI, From accessible to inaccessible cardinals, Fundamenta Mathematicae, vol. 53, pp. 225-308, corrections vol. 57 (1965), p. 119; reprinted in Tarski [1986] vol. 4, pp. 129-213.
195. [1964] H. JEROME KEISLER and ALFRED TARSKI, From accessible to inaccessible cardinals, Fundamenta Mathematicae, vol. 53, pp. 225-308, corrections vol. 57 (1965), p. 119; reprinted in Tarski [1986] vol. 4, pp. 129-213.
196. [1964] H. JEROME KEISLER and ALFRED TARSKI, From accessible to inaccessible cardinals, Fundamenta Mathematicae, vol. 53, pp. 225-308, corrections vol. 57 (1965), p. 119; reprinted in Tarski [1986] vol. 4, pp. 129-213.
197. [1927] DÉNES KÖNIG, Über eine Schlussweise aus dem Endlichen ins Unendliche: Punktmengen. Kartenfärben. Verwandtschaftsbeziehungen. Schachspiel, Acta Litterarum ac Scientiarum Regiae Universitatis Hungaricae Francisco-Josephinae, sectio scientiarum mathematicarum, vol. 3, pp. 121-130.
198. [1905] JULIUS (GYULA) KÖNIG, Zum Kontinuum-Problem, Verhandlungen des Dritten Internationalen Mathematiker-Kongresses in Heidelberg vom 8. bis 13. August 1904 (A. Krazer, editor), B. G. Teubner, Leipzig, reprinted in Mathematische Annalen, vol. 60 (1905), pp. 177-180 and Berichtigung, p. 462, pp. 144-147.
199. [1905] JULIUS (GYULA) KÖNIG, Zum Kontinuum-Problem, Verhandlungen des Dritten Internationalen Mathematiker-Kongresses in Heidelberg vom 8. bis 13. August 1904 (A. Krazer, editor), B. G. Teubner, Leipzig, reprinted in Mathematische Annalen, vol. 60 (1905), pp. 177-180 and Berichtigung, p. 462, pp. 144-147.
200. [1905] JULIUS (GYULA) KÖNIG, Zum Kontinuum-Problem, Verhandlungen des Dritten Internationalen Mathematiker-Kongresses in Heidelberg vom 8. bis 13. August 1904 (A. Krazer, editor), B. G. Teubner, Leipzig, reprinted in Mathematische Annalen, vol. 60 (1905), pp. 177-180 and Berichtigung, p. 462, pp. 144-147.
201. [1971] GEORG KREISEL, Observations on popular discussions of foundations, in Scott [1971], pp. 189-198.
202. [1980] KENNETH KUNEN, Set theory. An introduction to independence proofs, North-Holland, Amsterdam.
203. [1984] Kenneth Kunen and Jerry E. Vaughan (editors), Handbook of set-theoretic topology, North-Holland, Amsterdam.
204. [1921] KAZIMIERZ KURATOWSKI, Sur la notion de l'ordre dans la théorie des ensembles, Fundamente Mathematicae, vol. 2, pp. 161-171, reprinted in [1988] below, pp. 1-11,
205. [1921] KAZIMIERZ KURATOWSKI, Sur la notion de l'ordre dans la théorie des ensembles, Fundamente Mathematicae, vol. 2, pp. 161-171, reprinted in [1988] below, pp. 1-11,
206. [1922] _, Une méthode d'élimination des nombres transfinis des raisonnements mathématiques, Fundamenta Mathematicae, vol. 3, pp. 76-108.
207. [1988] _, Selected papers, Państwowe Wydawnictwo Naukowe, Warsaw, edited by Karol Borsuk and others.
208. [1931] KAZIMIERZ KURATOWSKI and ALFRED TARSKI, Les opérations logiques et les ensembles projectifs, Fundamenta Mathematicae, vol. 17, pp. 240-248, reprinted in Tarski [1986] vol. 1, pp. 551-559, and in Kuratowski [1988], pp. 367-375; translated in Tarski [1983], pp. 143-151.
209. [1931] KAZIMIERZ KURATOWSKI and ALFRED TARSKI, Les opérations logiques et les ensembles projectifs, Fundamenta Mathematicae, vol. 17, pp. 240-248, reprinted in Tarski [1986] vol. 1, pp. 551-559, and in Kuratowski [1988], pp. 367-375; translated in Tarski [1983], pp. 143-151.
210. [1931] KAZIMIERZ KURATOWSKI and ALFRED TARSKI, Les opérations logiques et les ensembles projectifs, Fundamenta Mathematicae, vol. 17, pp. 240-248, reprinted in Tarski [1986] vol. 1, pp. 551-559, and in Kuratowski [1988], pp. 367-375; translated in Tarski [1983], pp. 143-151.
211. [1931] KAZIMIERZ KURATOWSKI and ALFRED TARSKI, Les opérations logiques et les ensembles projectifs, Fundamenta Mathematicae, vol. 17, pp. 240-248, reprinted in Tarski [1986] vol. 1, pp. 551-559, and in Kuratowski [1988], pp. 367-375; translated in Tarski [1983], pp. 143-151.
212. [1935] DJURO R. KUREPA, Ensembles ordonnés et ramifiés. Thèse, Paris, published as Publications mathématiques de l'Université de Belgrade, vol. 4, pp. 1-138.
213. [1942] _, A propos d'une généralisation de la notion d'ensembles bien ordonnés, Acta Mathematica, vol. 75, pp. 139-150.
214. [1959] _, On the cardinal number of ordered sets and of symmetrical structures in dependence on the cardinal numbers of its chains and antichains, Glasnik Matematičko-fizički i astronomski, Periodicum mathematico-physicum et astronomicum, vol. 14, pp. 183-203.
215. [1962] HANS LÄUCHLI, Auswahlaxiom in der Algebra, Commentarii Mathematici Helvetici, vol. 37, pp. 1-18.
216. [1994] SHAUGHAN M. LAVINE, Understanding the infinite, Harvard University Press, Cambridge.
217. [1902] HENRI LEBESGUE, Intégrale, longueur, aire, Annali di Matematica Pura ed Applicata, vol. (3)7, pp. 231-359, reprinted in [1972] below, vol. 1, pp. 203-331.
218. [1902] HENRI LEBESGUE, Intégrale, longueur, aire, Annali di Matematica Pura ed Applicata, vol. (3)7, pp. 231-359, reprinted in [1972] below, vol. 1, pp. 203-331.
219. [1905] _, Sur les fonctions représentables analytiquement, Journal de Mathématiques Pures et Appliquées, vol. (6)1, pp. 139-216, reprinted in [1972] below, vol. 3, p. 103-180.
220. [1905] _, Sur les fonctions représentables analytiquement, Journal de Mathématiques Pures et Appliquées, vol. (6)1, pp. 139-216, reprinted in [1972] below, vol. 3, p. 103-180.
221. [1972] _, Oeuvres scientifiques, Kundig, Geneva.
222. [1957] AZRIEL LEVY, Indépendance conditionelle de V = L et d'axiomes qui se rattachent au système de M. Gödel, Comptes Rendus Hebdomadaires des Séances de l'Académie des Sciences, Paris, vol. 245, pp. 1582-1583.
223. [1960] _, Axiom schemata of strong infinity in axiomatic set theory, Pacific Journal of Mathematics, vol. 10, pp. 223-238.
224. [1960a] _, Principles of reflection in axiomatic set theory, Fundamenta Mathematicae, vol. 49, pp. 1-10.
225. [1963] _, Independence results in set theory by Cohen's method. I, III, IV (abstracts), Notices of the American Mathematical Society, vol. 10, pp. 592-593.
226. [1964] _, Measurable cardinals and the continuum hypothesis (abstract), Notices of the American Mathematical Society, vol. 11, pp. 769-770.
227. [1965] _, Definability in axiomatic set theory I, Logic, methodology and philosophy of science (Yehoshua Bar-Hillel, editor), Proceedings of the 1964 International Congress, Jerusalem, North-Holland, Amsterdam, pp. 127-151.
228. [1970] _, Definability in axiomatic set theory II, Mathematical logic and foundations of set theory (Yehoshua Bar-Hillel, editor), North-Holland, Amsterdam, pp. 129-145.
229. [1967] AZRIEL LEVY and ROBERT M. SOLOVAY, Measurable cardinals and the Continuum Hypothesis, Israel Journal of Mathematics, vol. 5, pp. 234-248.
230. [1905] ERNST LINDELÖF, Remarques sur un théorème fondamental de la théorie des ensembles, Acta Mathematica, vol. 29, pp. 183-190.
231. [1926] ADOLF LINDENBAUM and ALFRED TARSKI, Communication sur les recherches de la théorie des ensembles, Sprawozdana z Posiedzeń Towarzystwa Naukowego Warszawskiego, Wydział III, Nauk Matematyczno-fizycznych (Comptes Rendus des Séances de la Société des Sciences et des Lettres de Varsovie, Classe III, Sciences Mathématiques et Physiques), vol. 19, pp. 299-330, reprinted in Tarski [1986] vol. 1, pp. 171-204.
232. [1926] ADOLF LINDENBAUM and ALFRED TARSKI, Communication sur les recherches de la théorie des ensembles, Sprawozdana z Posiedzeń Towarzystwa Naukowego Warszawskiego, Wydział III, Nauk Matematyczno-fizycznych (Comptes Rendus des Séances de la Société des Sciences et des Lettres de Varsovie, Classe III, Sciences Mathématiques et Physiques), vol. 19, pp. 299-330, reprinted in Tarski [1986] vol. 1, pp. 171-204.
233. [1844] JOSEPH LIOUVILLE, Des remarques relatives 1° à des classes très-étendues de quantités dont la valeur n'est ni rationelle ni même réductible à des irrationnelles algébriques; 2° à un passage du livre des Principes où Newton calcule l'action exercée par une sphère sur un point extérieur, Comptes Rendus Hebdomadaires des Séances de l'Académie des Sciences, Paris, vol. 18, pp. 883-885.
234. [1851] _, Sur des classes très-étendues de quantités dont la valeur n'est ni algébrique ni même réductible à des irrationnelles algébriques, Journal de Mathématiques Pures et Appliquées, vol. 16, pp. 133-142.
235. [1955] JERZY ŁOŚ, Quelques remarques, théorèmes et problèmes sur les classes définissables d'algèbres, Mathematical interpretation of formal systems (Thoralf Skolem et al., editors), North-Holland, Amsterdam, pp. 98-113.
236. [1915] LEOPOLD LÖWENHEIM, Über Möglichkeiten im Relativkalkul, Mathematische Annalen, vol. 76, pp. 447-470, translated in van Heijenoort [1967], pp. 228-251.
237. [1915] LEOPOLD LÖWENHEIM, Über Möglichkeiten im Relativkalkul, Mathematische Annalen, vol. 76, pp. 447-470, translated in van Heijenoort [1967], pp. 228-251.
238. [1914] NIKOLAI N. LUZIN, Sur un problème de M. Baire, Comptes Rendus Hebdomadaires des Séances de l'Académie des Sciences, Paris, vol. 158, pp. 1258-1261.
239. [1917] _, Sur la classification de M. Baire, Comptes Rendus Hebdomadaires des Séances de l'Académie des Sciences, Paris, vol. 164, pp. 91-94.
240. [1925] _, Sur un problème de M. Emile Borel et les ensembles projectifs de M. Henri Lebesgue; les ensembles analytiques, Comptes Rendus Hebdomadaires des Séances de l'Académie des Sciences, Paris, vol. 180, pp. 1318-1320.
241. [1925a] _, Sur les ensembles projectifs de M. Henri Lebesgue, Comptes Rendus Hebdomadaires des Séances de l'Académie des Sciences, Paris, vol. 180, pp. 1572-1574.
242. [1925b] _, Les propriétés des ensembles projectifs, Comptes Rendus Hebdomadaires des Séances de l'Académie des Sciences, Paris, vol. 180, pp. 1817-1819.
243. [1918] NIKOIJVI N. LUZIN and WACłAW SIERPIŃSKI, Sur quelques propriétés des ensembles (A), Bulletin de l'Académie des Sciences de Cracovie, Classe des Sciences Mathématiques et Naturelles, Série A, pp. 35-48, reprinted in Sierpiński [1975], pp. 192-204.
244. [1918] NIKOIJVI N. LUZIN and WACłAW SIERPIŃSKI, Sur quelques propriétés des ensembles (A), Bulletin de l'Académie des Sciences de Cracovie, Classe des Sciences Mathématiques et Naturelles, Série A, pp. 35-48, reprinted in Sierpiński [1975], pp. 192-204.
245. [1923] _, Sur un ensemble non mesurable B, Journal de Mathématiques Pures et Appliquées, vol. (9)2, pp. 53-72, reprinted in Sierpiński [1975], pp. 504-519.
246. [1923] _, Sur un ensemble non mesurable B, Journal de Mathématiques Pures et Appliquées, vol. (9)2, pp. 53-72, reprinted in Sierpiński [1975], pp. 504-519.
247. [1911] PAUL MAHLO, Über lineare transfinite Mengen, Berichte über die Verhandlungen der Königlich Sächsischen Gesellschaft der Wissenschaften zu Leipzig Mathematische-Physische Klasse, vol. 63, pp. 187-225.
248. 0-Zalen, Berichte über die Verhandlungen der Königlich Sächsischen Gesellschaft der Wissenschaften zu Leipzig Mathematische-Physische Klasse, vol. 64, pp. 108-112.
249. 0-Zahlen II, Berichte über die Verhandlungen der Königlich Sächsischen Gesellschaft der Wissenschaften zu Leipzig, Mathematische-Physische Klasse, vol. 65, pp. 268-282.
250. [1913a] _, Über Teilmengen des Kontinuums von dessen Mächtigkeit, Berichte über die Verhandlungen der Königlich Sächsischen Gesellschaft der Wissenschaften zu Leipzig, Mathematische-Physische Klasse, vol. 65, pp. 283-315.
251. 2, Israel Journal of Mathematics, vol. 9, pp. 367-379.
252. 3 sets of reals, Annals of Mathematics, vol. 89, pp. 138-159.
253. [1983] HERBERT MESCHKONVSKI, Georg Cantor. Leben. Werk und Wirkung, Bibliographisches Institut, Mannheim.
254. [1991] Herbert Meschkowski and Winfried Nilson (editors), Briefe / Georg Cantor, Springer-Verlag, Berlin.
255. [1984] ARNOLD W. MILLER, Special subsets of the real line, in Kunen-Vaughan [1984], pp. 201-233.
256. [1917] DIMITRY MIRIMANOEE, Les antinomies de Russell et de Burali-Forti et le problème fondamental de la théorie des ensembles, L'Enseignment Mathématique, vol. 19, pp. 37-52.
257. [1917a] _, Remarques sur la théorie des ensembles et les antinomies Cantoriennes. I, L'Enseignment Mathématique, vol. 19, pp. 209-217.
258. [1956] RICHARD M. MONTAGUE, Zermelo-Fraenkel set theory is not a finite extension of Zermelo set theory (abstract), Bulletin of the American Mathematical Society, vol. 62, p. 260.
259. [1961] _, Fraenkel's addition to the axioms of Zermelo, in Bar-Hillel-Poznanski-Rabin-Robinson [1961], pp. 91-114.
260. [1982] GREGORY H. MOORI, Zermelo's Axiom of Choice. Its origins, development and influence, Springer-Verlag, New York.
261. [1988] _, The roots of Russell's paradox, Russell, vol. 8, pp. 46-56, (new series).
262. [1988a] _, The origins of forcing, Logic colloquium '86 (Frank R. Drake and John K. Truss, editors), North-Holland, Amsterdam, pp. 143-173.
263. [1988b] _, The emergence of first-order logic, History and philosophy of modern mathematics (William Aspray and Philip Kitcher, editors), Minnesota Studies in the Philosophy of Science, vol. 11, University of Minnesota Press, Minneapolis, pp. 95-135.
264. [1989] _, Towards a history of Cantor's Continuum Problem, The history of modern mathematics. Vol. 1: Ideas and their reception (David E. Rowe and John McCleary, editors), Academic Press, Boston, pp. 79-121.
265. [1981] GREGORY H. MOORE and ALEJANDRO R. GARCIADIEGO, Burali-Forti'sparadox: A reappraisal of its origins, Historia Mathematica, vol. 8, pp. 319-350.
266. [1980] YIANNIS MOSCHOVAKIS, Descriptive set theory, North-Holland, Amsterdam.
267. [1939] ANDRZEJ M. MOSTOWSKI, Über die Unabhängigkeit des Wohlordnungssatzes vom Ordnungsprinzip, Fundamenta Mathematicae, vol. 32, pp. 201-252, translated in [1979] below, vol. 1, pp. 290-338.
268. [1939] ANDRZEJ M. MOSTOWSKI, Über die Unabhängigkeit des Wohlordnungssatzes vom Ordnungsprinzip, Fundamenta Mathematicae, vol. 32, pp. 201-252, translated in [1979] below, vol. 1, pp. 290-338.
269. [1949] _, An undecidable arithmetical statement, Fundamenta Mathematicae, vol. 36, pp. 143-164, reprinted in [1979] below, vol. 1, pp. 531-552.
270. [1949] _, An undecidable arithmetical statement, Fundamenta Mathematicae, vol. 36, pp. 143-164, reprinted in [1979] below, vol. 1, pp. 531-552.
271. [1979] _, Foundational studies. Selected works, North-Holland, Amsterdam, edited by Kazimierz Kuratowski and others.
272. [1971] JOHN R. MYHILL and DANA S. SCOTT, Ordinal definability, in Scott [1971], pp. 271-278.
273. [1990] JAROSLAV NEŠETŘIL and VOJTĚCH RÖDL, Mathematics of Ramsey theory, Springer-Verlag, Berlin.
274. [1937] Emmy Noether and Jean Cavaillès (editors), Briefwechsel Cantor-Dedekind, Hermann, Paris, translated into French in Cavaillès [1962].
275. [1971] JOHN C. OXTOBY, Measure and category. A survey of the analogies between topological and measure spaces. Springer-Verlag, New York.
276. [1977] CHARLES PARSONS, What is the iterative concept of set?, Logic, foundations of mathematics and computability theory (Robert E. Butts and Jaakko Hintikka, editors), Proceedings of the Fifth International Congress of Logic, Methodology and the Philosophy of Science (London, Ontario 1975), The University of Western Ontario Series in Philosophy and Science, vol. 9, D. Reidel, Dordrecht, pp. 335-367, reprinted in Benacerraf-Putnam [1983], pp. 503-529.
277. [1977] CHARLES PARSONS, What is the iterative concept of set?, Logic, foundations of mathematics and computability theory (Robert E. Butts and Jaakko Hintikka, editors), Proceedings of the Fifth International Congress of Logic, Methodology and the Philosophy of Science (London, Ontario 1975), The University of Western Ontario Series in Philosophy and Science, vol. 9, D. Reidel, Dordrecht, pp. 335-367, reprinted in Benacerraf-Putnam [1983], pp. 503-529.
278. [1977] CHARLES PARSONS, What is the iterative concept of set?, Logic, foundations of mathematics and computability theory (Robert E. Butts and Jaakko Hintikka, editors), Proceedings of the Fifth International Congress of Logic, Methodology and the Philosophy of Science (London, Ontario 1975), The University of Western Ontario Series in Philosophy and Science, vol. 9, D. Reidel, Dordrecht, pp. 335-367, reprinted in Benacerraf-Putnam [1983], pp. 503-529.
279. [1897] GUISEPPE PEANO, Studii di logica matematica, Atti della Accademia delle scienze di Torino, Classe di scienze fisiche, matematiche e naturali, vol. 32, pp. 565-583, reprinted in [1958] below, pp. 201-217.
280. [1897] GUISEPPE PEANO, Studii di logica matematica, Atti della Accademia delle scienze di Torino, Classe di scienze fisiche, matematiche e naturali, vol. 32, pp. 565-583, reprinted in [1958] below, pp. 201-217.
281. [1905-8] _, Formulario mathematico, Bocca, Torino, reprinted Edizioni Cremonese, Rome, 1960.
282. [1905-8] _, Formulario mathematico, Bocca, Torino, reprinted Edizioni Cremonese, Rome, 1960.
283. [1911] _, Sulla definitions di funzione, Atti della Accademia nazionale dei Lincei, Rendiconti, Classe di scienze fisiche, matematiche e naturali, vol. 20-1, pp. 3-5.
284. [1913] _, Review of: A.N. Whitehead and B. Russell, Principia Mathematica, vols. I,II, Bollettino di bibliografia e storia delle scienze matematiche (Loria), vol. 15, pp. 47-53, 75-81, reprinted in [1958] below, pp. 389-401.
285. [1913] _, Review of: A.N. Whitehead and B. Russell, Principia Mathematica, vols. I,II, Bollettino di bibliografia e storia delle scienze matematiche (Loria), vol. 15, pp. 47-53, 75-81, reprinted in [1958] below, pp. 389-401.
286. [1913] _, Review of: A.N. Whitehead and B. Russell, Principia Mathematica, vols. I,II, Bollettino di bibliografia e storia delle scienze matematiche (Loria), vol. 15, pp. 47-53, 75-81, reprinted in [1958] below, pp. 389-401.
287. [1958] _, Opere scelte, vol. 2, Edizioni Cremonese, Rome.
288. [1990] VOLKER PECKHAUS, "Ich habe mich wohl gehütet alle Patronen auf einmal zu verschiessen." Ernst Zermelo in Göttingen, History and Philosophy of Logic, vol. 11, pp. 19-58.
289. [1883] CHARLES S. PEIRCE, A theory of probable inference. Note B. The logic of relativen, Studies in Logic by Members of the John Hopkins University, pp. 187-203, reprinted in Charles Hartshorne and Paul Weiss (editors). Collected Papers of Charles Sanders Peirce, vol. 3, Harvard University Press, Cambridge, pp. 195-209.
290. [1883] CHARLES S. PEIRCE, A theory of probable inference. Note B. The logic of relativen, Studies in Logic by Members of the John Hopkins University, pp. 187-203, reprinted in Charles Hartshorne and Paul Weiss (editors). Collected Papers of Charles Sanders Peirce, vol. 3, Harvard University Press, Cambridge, pp. 195-209.
291. [1972] DAVID PINCUS, Zermelo-Fraenkel consistency results by Fraenkel-Mostowski methods, The Journal of Symbolic Logic, vol. 37, pp. 721-743.
292. [1969] M. PINL, Kollegen in einer dunklen Zeit, Jahresbericht der Deutschen Mathematiker-Vereinigung, vol. 71, pp. 167-228.
293. [1990] MICHAEL D. POTTER, Sets. An introduction, Clarendon Press, Oxford.
294. [1989] WALTER PURKERT, Cantor's views on the foundations of mathematics, The history of modern mathematics. Vol. 1: Ideas and their reception (David E. Rowe and John McCleary, editors), Academic Press, Boston, pp. 49-65.
295. [1987] WALTER PURKERT and HANS J. ILGAUDS, Georg Cantor: 1845-1918, Birkhäuser Verlag, Basel.
296. [1960] WILLARD V. O. QUINE, Word and object, MIT Press, Cambridge.
297. [1984] JEAN RAISONNIER, A mathematical proof of S. Shelah's theorem on the measure problem and related results, Israel Journal of Mathematics, vol. 48, pp. 48-56.
298. [1930] FRANK P. RAMSEY, On a problem of formal logic, Proceedings of the London Mathematical Society, vol. (2)30, pp. 264-286, reprinted in Gessel-Rota [1987], pp. 2-24.
299. [1930] FRANK P. RAMSEY, On a problem of formal logic, Proceedings of the London Mathematical Society, vol. (2)30, pp. 264-286, reprinted in Gessel-Rota [1987], pp. 2-24.
300. [1981] BERNHARD RANG and WOLFGANG THOMAS, Zermelo's discovery of the "Russell paradox", Historia Mathematica, vol. 8, pp. 15-22.
301. [1951] ABRAHAM ROBINSON, On the metamathematics of algebra, North Holland, Amsterdam.
302. [1947] RAPHAEL M. ROBINSON, On the decomposition of spheres, Fundamenta Mathematicae, vol. 34, pp. 246-270.
303. [1938] FRITZ ROTHBERGER, Eine Äquivalenz zwischen der Kontinuumhypothese und der Existenz der Lusinschen und Sierpińskischen Mengen, Fundamenta Mathematicae, vol. 30, pp. 215-217.
304. [1939] _, Sur un ensemble toujours de première categorie qui est depourvu de la properté λ, Fundamenta Mathematicae, vol. 32, pp. 294-300.
305. [1948] _, On some problems of Hausdorff and Sierpiński, Fundamenta Mathematicae, vol. 35, pp. 29-46.
306. [1985] HERMAN RUBIN and JEAN E. RUBIN, Equivalents of the Axiom of Choice, II, North-Holland, Amsterdam, revised, expanded version of their Equivalents of the Axiom of Choice, North-Holland, Amsterdam, 1963.
307. [1985] HERMAN RUBIN and JEAN E. RUBIN, Equivalents of the Axiom of Choice, II, North-Holland, Amsterdam, revised, expanded version of their Equivalents of the Axiom of Choice, North-Holland, Amsterdam, 1963.
308. [1903] BERTRAND A. W. RUSSELL, The principles of mathematics, Cambridge University Press, Cambridge, later editions, George Allen & Unwin, London.
309. [1906] _, On some difficulties in the theory of transfinite numbers and order types, Proceedings of the London Mathematical Society, vol. (2)4, pp. 29-53. reprinted in [1973] below, pp. 135-164.
310. [1906] _, On some difficulties in the theory of transfinite numbers and order types, Proceedings of the London Mathematical Society, vol. (2)4, pp. 29-53. reprinted in [1973] below, pp. 135-164.
311. [1959] _, My philosophical development, George Allen & Unwin. London.
312. [1973] _, Essays in analysis, George Braziller, New York, edited by Douglas Lackey.
313. [1890] ERNST SCHRÖDER, Vorlesungen über die Algebra der Logik (exakte Logik), vol. 1, B. G. Teubner, Leipzig, reprinted in [1966] below.
314. [1895] _, Vorlesungen über die Algebra der Logik (exakte Logik). Vol. 3: Algebra und Logik der Relative, B. G. Teubner, Leipzig, reprinted in [1966] below.
315. [1966] _, Vorlesungen über die Algebra der Logik, Chelsea, New York, three volumes.
316. [1961] DANA S. SCOTT, Measurable cardinals and constructible sets, Bulletin de l'Académie Polonaise des Sciences, Série des Sciences Mathématiques, Astronomiques et Physiques, vol. 9, pp. 521-524.
317. [1967] _, A proof of the independence of the Continuum Hypothesis, Mathematical Systems Theory, vol. 1, pp. 89-111.
318. [1971] Dana S. Scott (editor), Axiomatic set theory, Proceedings of Symposia in Pure Mathematics vol. 13, part 1, American Mathematical Society, Providence.
319. [1974] _, Axiomatizing set theory, Axiomatic set theory (Thomas J. Jech, editor), Proceedings of Symposia in Pure Mathematics vol. 13, part 2, American Mathematical Society, Providence, pp. 207-214.
320. [1980] SAHARON SHELAH, Going to Canossa (abstract), Abstracts of papers presented to the American Mathematical Society, vol. 1, p. 630.
321. [1984] _, Can you take Solovay's inaccessible away?, Israel Journal of Mathematics, vol. 48, pp. 1-47.
322. [1951] JOHN C. SHEPHERDSON, Inner models for set theory - Part I, The Journal of Symbolic Logic, vol. 16, pp. 161-190.
323. [1952] _, Inner models far set theory - Part II, The Journal of Symbolic Logic, vol. 17, pp. 225-237.
324. [1953] _, Inner models for set theory - Part III, The Journal of Symbolic Logic, vol. 18, pp. 145-167.
325. [1959] JOSEPH R. SHOENFIELD, On the independence of the axiom of constructibility, American Journal of Mathematics, vol. 81, pp. 537-540.
326. [1967] _, Mathematical logic, Addison-Wesley, Reading.
327. [1971] _, Unramified forcing, in Scott [1971], pp. 357-381.
328. [1977] _, Axioms of set theory, Handbook of mathematical logic (K. Jon Barwise, editor), North-Holland, Amsterdam, pp. 321-344.
329. [1918] WACłAW SIERPIŃSKI, L'axiome de M. Zermelo et son râle dans la théorie des ensembles et l'analyse, Bulletin de l'Académie des Sciences de Cracovie, Classe des Sciences Mathématiques et Naturelles, Série A, pp. 97-152, reprinted in [1975] below, pp. 208-255.
330. [1918] WACłAW SIERPIŃSKI, L'axiome de M. Zermelo et son râle dans la théorie des ensembles et l'analyse, Bulletin de l'Académie des Sciences de Cracovie, Classe des Sciences Mathématiques et Naturelles, Série A, pp. 97-152, reprinted in [1975] below, pp. 208-255.
331. 1), Fundamenta Mathematicae, vol. 5, pp. 177-187, reprinted in [1975] below, pp. 527-536.
332. 1), Fundamenta Mathematicae, vol. 5, pp. 177-187, reprinted in [1975] below, pp. 527-536.
333. [1925] _, Sur une class d'ensembles, Fundamenta Mathematicae, vol. 7, pp. 237-243, reprinted in [1975] below, pp. 571-576.
334. [1925] _, Sur une class d'ensembles, Fundamenta Mathematicae, vol. 7, pp. 237-243, reprinted in [1975] below, pp. 571-576.
335. [1928] _, Sur un ensemble non dénombrable, dont toute image continue est de mesure nulle, Fundamenta Mathematicae, vol. 11, pp. 302-304, reprinted in [1975] below, pp. 702-704.
336. [1928] _, Sur un ensemble non dénombrable, dont toute image continue est de mesure nulle, Fundamenta Mathematicae, vol. 11, pp. 302-304, reprinted in [1975] below, pp. 702-704.
337. [1934] _, Hypothèse du continu, Monografie Matematyczne, vol. 4, Warsaw, second revised edtion, Chelsea, New York, 1956.
338. [1975] _, Oeuvres choisies, vol. 2, Państwowe Wydawnictwo Naukowe, Warsaw, edited by Stanislaw Hartman and others.
339. [1976] _, Ouevres choisies, vol. 3, Państwowe Wydawnictwo Naukowe, Warsaw, edited by Stanisław Hartman and others.
340. [1930] WACłAW SIERPIŃSKI and ALFRED TARSKI, Sur une propriété caractéristique des nombres inaccessibles, Fundamenta Mathematicae, vol. 15, pp. 292-300, reprinted in Sierpiński [1976], pp. 29-35 and in Tarski [1986] vol. 1, pp. 289-297.
341. [1930] WACłAW SIERPIŃSKI and ALFRED TARSKI, Sur une propriété caractéristique des nombres inaccessibles, Fundamenta Mathematicae, vol. 15, pp. 292-300, reprinted in Sierpiński [1976], pp. 29-35 and in Tarski [1986] vol. 1, pp. 289-297.
342. [1930] WACłAW SIERPIŃSKI and ALFRED TARSKI, Sur une propriété caractéristique des nombres inaccessibles, Fundamenta Mathematicae, vol. 15, pp. 292-300, reprinted in Sierpiński [1976], pp. 29-35 and in Tarski [1986] vol. 1, pp. 289-297.
343. [1920] THORALF SKOLEM, Logisch-kombinatorische Untersuchungen über die Erfüllbarkeit oder Beweisbarkeit mathematischer Sätze nebst einem Theoreme über dichte Mengen, Videnskaps-selskapets Skrifler, I, Matematisk-Naturvidenskabelig Klass, no. 4, pp. 1-36, reprinted in [1970] below, pp. 103-136; partially translated in van Heijenoort [1967], pp. 252-263.
344. [1920] THORALF SKOLEM, Logisch-kombinatorische Untersuchungen über die Erfüllbarkeit oder Beweisbarkeit mathematischer Sätze nebst einem Theoreme über dichte Mengen, Videnskaps-selskapets Skrifler, I, Matematisk-Naturvidenskabelig Klass, no. 4, pp. 1-36, reprinted in [1970] below, pp. 103-136; partially translated in van Heijenoort [1967], pp. 252-263.
345. [1920] THORALF SKOLEM, Logisch-kombinatorische Untersuchungen über die Erfüllbarkeit oder Beweisbarkeit mathematischer Sätze nebst einem Theoreme über dichte Mengen, Videnskaps-selskapets Skrifler, I, Matematisk-Naturvidenskabelig Klass, no. 4, pp. 1-36, reprinted in [1970] below, pp. 103-136; partially translated in van Heijenoort [1967], pp. 252-263.
346. [1923] _, Einige Bemerkungen zur axiomatischen Begründung der Mengenlehre, Matematikerkongressen i Helsingfors den 4-7 Juli 1922, Den femte skandinaviska matematikerkongressen, Redogörelse, Akademiska-Bokhandeln, Helsinki, pp. 217-232, reprinted in [1970] below, pp. 137-152; translated in van Heijenoort [1967], pp. 290-301.
347. [1923] _, Einige Bemerkungen zur axiomatischen Begründung der Mengenlehre, Matematikerkongressen i Helsingfors den 4-7 Juli 1922, Den femte skandinaviska matematikerkongressen, Redogörelse, Akademiska-Bokhandeln, Helsinki, pp. 217-232, reprinted in [1970] below, pp. 137-152; translated in van Heijenoort [1967], pp. 290-301.
348. [1923] _, Einige Bemerkungen zur axiomatischen Begründung der Mengenlehre, Matematikerkongressen i Helsingfors den 4-7 Juli 1922, Den femte skandinaviska matematikerkongressen, Redogörelse, Akademiska-Bokhandeln, Helsinki, pp. 217-232, reprinted in [1970] below, pp. 137-152; translated in van Heijenoort [1967], pp. 290-301.
349. [1930] _, Einige Bemerkungen zu der Abhandlung von E. Zermelo: "Über die Definitheit in der Axiomatik", Fundamenta Mathematicae, vol. 15, pp. 337-341, reprinted in [1970] below, pp. 275-279.
350. [1930] _, Einige Bemerkungen zu der Abhandlung von E. Zermelo: "Über die Definitheit in der Axiomatik", Fundamenta Mathematicae, vol. 15, pp. 337-341, reprinted in [1970] below, pp. 275-279.
351. [1933] _, Ein kombinatorischer Satz mit Anwendung auf ein logisches Entscheidungsproblem, Fundamenta Mathematicae, vol. 20, pp. 254-261, reprinted in [1970] below, pp. 337-344.
352. [1933] _, Ein kombinatorischer Satz mit Anwendung auf ein logisches Entscheidungsproblem, Fundamenta Mathematicae, vol. 20, pp. 254-261, reprinted in [1970] below, pp. 337-344.
353. [1933a] _, Über die Unmöglichkeit einer vollständigen Charakterisierung der Zahlenreihe mittels eines endlichen Axiomensystems, Norsk Matematisk Forenings Skrifler, vol. 2, no. 10, pp. 73-82, reprinted in [1970] below, pp. 345-354.
354. [1933a] _, Über die Unmöglichkeit einer vollständigen Charakterisierung der Zahlenreihe mittels eines endlichen Axiomensystems, Norsk Matematisk Forenings Skrifler, vol. 2, no. 10, pp. 73-82, reprinted in [1970] below, pp. 345-354.
355. [1934] _, Über die Nichl-charakterisierbarkeit der Zahlenreihe mittels endlich oder abzählbar unendlich vieler Assagen mit ausschliesslich Zahlenvariablen, Fundamenta Mathematicae, vol. 23, pp. 150-161, reprinted in [1970] below, pp. 355-366.
356. [1934] _, Über die Nichl-charakterisierbarkeit der Zahlenreihe mittels endlich oder abzählbar unendlich vieler Assagen mit ausschliesslich Zahlenvariablen, Fundamenta Mathematicae, vol. 23, pp. 150-161, reprinted in [1970] below, pp. 355-366.
357. [1970] _, Selected works in logic, Univesitetsforlaget, Oslo, edited by Jens E. Fenstad.
358. [1963] ROBERT M. SOLOVAY, Independence results in the theory of cardinals. I, II (abstracts), Notices of the American Mathematical Society, vol. 10, p. 595.
359. א0 can be anything it ought to be (abstract), in Addison-Henkin-Tarski [1965], p. 435.
360. [1965a] _, Measurable cardinals and the continuum hypothesis (abstract), Notices of the American Mathematical Society, vol. 12, p. 132.
361. [1965b] _, The measure problem (abstract), Notices of the American Mathematical Society, vol. 12, p. 217.
362. 2 sets of reals, Foundations of mathematics (Jack J. Bulloff, Thomas C. Holyoke, and Samuel W. Hahn, editors), Symposium papers commemorating the sixtieth birthday of Kurt Gödel, Springer-Verlag, Berlin, pp. 58-73.
363. [1970] _, A model of set theory in which every set of reals is Lebesgue measurable, Annals of Mathematics, vol. 92, pp. 1-56.
364. [1957] ERNST SPECKER. Zur Axiomatik der Mengenlehre (Fundierungs-und Auswahlaxiom), Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 3, pp. 173-210.
365. [1910] ERNST STEINITZ, Algebraische Theorie der Körper, Journal für die reine und angewandte Mathematik (Crelle's Journal), vol. 137, pp. 167-309.
366. [1917] MIKHAIL YA. SUSLIN, Sur une définition des ensembles mesurables B sans nombres transfinis, Comptes Rendus Hebdomadaires des Séances de l'Académie des Sciences, Paris, vol. 164, pp. 88-91.
367. [1920] _, Problème 3, Fundamenta Mathematicae, vol. 1, p. 223.
368. [1924] ALFRED TARSKI, Sur quelques théorèmes qui équivalent à l'axiome du choix, Fundamenta Mathematicae, vol. 5, pp. 147-154, reprinted in [1986] below, vol. 1, pp. 41-48.
369. [1924] ALFRED TARSKI, Sur quelques théorèmes qui équivalent à l'axiome du choix, Fundamenta Mathematicae, vol. 5, pp. 147-154, reprinted in [1986] below, vol. 1, pp. 41-48.
370. [1931] _, Sur les ensembles définissables de nombres réels, Fundamenta Mathematicae, vol. 17, pp. 210-239, translated in Tarski [1983], pp. 110-142.
371. [1931] _, Sur les ensembles définissables de nombres réels, Fundamenta Mathematicae, vol. 17, pp. 210-239, translated in Tarski [1983], pp. 110-142.
372. [1933] _, Pojȩcie prawdy w jȩzykach nauk dedukcyjnych. (the concept of truth in the languages of deductive sciences), Prace Towarzystwa Naukowego Warszawskiego, Wydział III, Nauk Matematyczno-fizyczych (Travaux de la Société des Sciences et des Lettres de Varsovie, Classe III, Sciences Mathématiques et Physiques), no. 34, see also [1935] below.
373. [1933] _, Pojȩcie prawdy w jȩzykach nauk dedukcyjnych. (the concept of truth in the languages of deductive sciences), Prace Towarzystwa Naukowego Warszawskiego, Wydział III, Nauk Matematyczno-fizyczych (Travaux de la Société des Sciences et des Lettres de Varsovie, Classe III, Sciences Mathématiques et Physiques), no. 34, see also [1935] below.
374. [1935] _, Der Wahrheitsbegriff in den formalisierten Sprachen, Studia Philosophica, vol. 1, pp. 261-405, German translation of [1933] with a postscript: reprinted in [1986] below, vol. 2, pp. 51-198; translated in [1983] below, pp. 152-278.
375. [1935] _, Der Wahrheitsbegriff in den formalisierten Sprachen, Studia Philosophica, vol. 1, pp. 261-405, German translation of [1933] with a postscript: reprinted in [1986] below, vol. 2, pp. 51-198; translated in [1983] below, pp. 152-278.
376. [1935] _, Der Wahrheitsbegriff in den formalisierten Sprachen, Studia Philosophica, vol. 1, pp. 261-405, German translation of [1933] with a postscript: reprinted in [1986] below, vol. 2, pp. 51-198; translated in [1983] below, pp. 152-278.
377. [1951] _, A decision method for elementary algebra and geometry, University of California Press, Berkeley, prepared by J. C. C. McKinsey, second revised edition.
378. [1962] _, Some problems and results relevant to the foundations of set theory, Logic, methodology and philosophy of science (Ernest Nagel, Patrick Suppes, and Alfred Tarski, editors), Stanford University Press, Stanford, pp. 125-135, reprinted in [1986] below, vol. 4, pp. 115-125.
379. [1962] _, Some problems and results relevant to the foundations of set theory, Logic, methodology and philosophy of science (Ernest Nagel, Patrick Suppes, and Alfred Tarski, editors), Stanford University Press, Stanford, pp. 125-135, reprinted in [1986] below, vol. 4, pp. 115-125.
380. [1983] _, Logic, semantics, metamathematics. papers from 1923 to 1938, second ed., Hackett, Indianapolis, translations by J. H. Woodger.
381. [1986] _, Collected papers, Birkhäuser, Basel, edited by Steven R. Givant and Ralph N. McKenzie.
382. [1984] STEVO TODORČEVIĆ, Trees and linearly ordered sets, in Kunen-Vaughan [1984], pp. 235-293.
383. [1930] STANISłAW M. ULAM, Zur Masstheorie in der allgemeinen Mengenlehre, Fundamenta Mathematicae, vol. 16, pp. 140-150, reprinted in [1974] below, pp. 9-19.
384. [1930] STANISłAW M. ULAM, Zur Masstheorie in der allgemeinen Mengenlehre, Fundamenta Mathematicae, vol. 16, pp. 140-150, reprinted in [1974] below, pp. 9-19.
385. [1974] _, Sets, numbers and universes, Selected Works, MIT Press, Cambridge, edited by W. A. Beyer, Jan Mycielski and Gian-Carlo Rota.
386. [1972] DIRK VAN DALEN and A.F. MONNA, Sets and integration. An outline of the development, Wolters-Noordhoff, Groningen.
387. [1984] ERIC K. VAN DOUWEN, The integers and topology, in Kunen-Vaughan [1984], pp. 111-168.
388. [1967] Jean van Heijenoort (editor). From Frege to Gödel: A source book in mathematical logic, 1879-1931, Harvard University Press, Cambridge.
389. [1990] JERRY VAUGHAN, Small uncountable cardinals and topology, Open problems in topology (Jan Van Mill and George M. Reed, editors). North-Holland, Amsterdam, pp. 195-218.
390. [1905] GUISEPPE VITALI, Sul problema della misura dei gruppi di punti di una retta, Bologna, Tip. Gamberini e Parmeggiani.
391. [1923] JOHN VON NEUMANN, Zur Einführung der transfiniten Zahlen, Acta Litterarum ac Scientiarum Regiae Universitatis Hungaricae Francisco-Josephinae, sectio scientiarum mathematicarum, vol. 1, pp. 199-208, reprinted in [1961] below, pp. 24-33; translated in van Heijenoort [1967], pp. 346-354.
392. [1923] JOHN VON NEUMANN, Zur Einführung der transfiniten Zahlen, Acta Litterarum ac Scientiarum Regiae Universitatis Hungaricae Francisco-Josephinae, sectio scientiarum mathematicarum, vol. 1, pp. 199-208, reprinted in [1961] below, pp. 24-33; translated in van Heijenoort [1967], pp. 346-354.
393. [1923] JOHN VON NEUMANN, Zur Einführung der transfiniten Zahlen, Acta Litterarum ac Scientiarum Regiae Universitatis Hungaricae Francisco-Josephinae, sectio scientiarum mathematicarum, vol. 1, pp. 199-208, reprinted in [1961] below, pp. 24-33; translated in van Heijenoort [1967], pp. 346-354.
394. [1925] _, Eine Axiomatisierung der Mengenlehre, Journal für die reine und angewandte Mathematik (Crelle's Journal), vol. 154, pp. 219-240, Berichtigung , vol. 155, p. 128; reprinted in [1961] below, pp. 34-56; translated in van Heijenoort [1967], pp. 393-413.
395. [1925] _, Eine Axiomatisierung der Mengenlehre, Journal für die reine und angewandte Mathematik (Crelle's Journal), vol. 154, pp. 219-240, Berichtigung , vol. 155, p. 128; reprinted in [1961] below, pp. 34-56; translated in van Heijenoort [1967], pp. 393-413.
396. [1925] _, Eine Axiomatisierung der Mengenlehre, Journal für die reine und angewandte Mathematik (Crelle's Journal), vol. 154, pp. 219-240, Berichtigung , vol. 155, p. 128; reprinted in [1961] below, pp. 34-56; translated in van Heijenoort [1967], pp. 393-413.
397. [1925] _, Eine Axiomatisierung der Mengenlehre, Journal für die reine und angewandte Mathematik (Crelle's Journal), vol. 154, pp. 219-240, Berichtigung , vol. 155, p. 128; reprinted in [1961] below, pp. 34-56; translated in van Heijenoort [1967], pp. 393-413.
398. [1928] _, Über die Definition durch transfinite Induktion und verwandte Fragen der allgemeinen Mengenlehre, Mathematische Annalen, vol. 99, pp. 373-391, reprinted in [1961] below, pp. 320-338.
399. [1928] _, Über die Definition durch transfinite Induktion und verwandte Fragen der allgemeinen Mengenlehre, Mathematische Annalen, vol. 99, pp. 373-391, reprinted in [1961] below, pp. 320-338.
400. [1928a] _, Die Axiomatisierung der Mengenlehre, Mathematische Zeitschrift, vol. 27, pp. 669-752, reprinted in [1961] below, pp. 339-422.
401. [1928a] _, Die Axiomatisierung der Mengenlehre, Mathematische Zeitschrift, vol. 27, pp. 669-752, reprinted in [1961] below, pp. 339-422.
402. [1929] _, Über eine Widerspruchfreiheitsfrage in der axiomaticschen Mengenlehre, Journal für die reine und angewandte Mathematik (Crelle's Journal), vol. 160, pp. 227-241, reprinted in [1961] below, pp. 494-508.
403. [1929] _, Über eine Widerspruchfreiheitsfrage in der axiomaticschen Mengenlehre, Journal für die reine und angewandte Mathematik (Crelle's Journal), vol. 160, pp. 227-241, reprinted in [1961] below, pp. 494-508.
404. [1961] _, John von Neumann. Collected works, vol. 1, Pergamon Press, New York, edited by Abraham H. Taub.
405. [1962] PETR VOPĚNKA, Construction of models of set theory by the method of ultraproducts (in Russian), Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 8, pp. 293-304.
406. [1964] _, The independence of the Continuum Hypothesis (in Russian), Commentationes Mathematicae Universitatis Carolinae, vol. 5, pp. 1-48, supplement I; translated in American Mathematical Society Translations, vol. 57 (1966), pp. 85-112.
407. [1964] _, The independence of the Continuum Hypothesis (in Russian), Commentationes Mathematicae Universitatis Carolinae, vol. 5, pp. 1-48, supplement I; translated in American Mathematical Society Translations, vol. 57 (1966), pp. 85-112.
408. [1967] _, The general theory of ∇-models, Commentationes Mathematicae Universitatis Carolinae, vol. 8, pp. 145-170.
409. [1985] STANLEY WAGON, The Banach-Tarski paradox, Encyclopedia of Mathematics and Its Applications, vol. 24, Cambridge University Press, Cambridge, paperback edition 1993.
410. [1974] HAO WANG, From mathematics to philosophy, Humanities Press, New York.
411. [1974a] _, The concept of set, in Wang [1974], pp. 181-223; reprinted in Benacerraf-Putnam [1983], pp. 530-570.
412. [1974a] _, The concept of set, in Wang [1974], pp. 181-223; reprinted in Benacerraf-Putnam [1983], pp. 530-570.
413. [1910] ALFRED N. WHITEHEAD and BERTRAND A. W. RUSSELL, Principia mathematica, vol. 1, Cambridge University Press, Cambridge.
414. [1912] _, Principia mathematica, vol. 2, Cambridge University Press, Cambridge.
415. [1913] _, Principia mathematica, vol. 3, Cambridge University Press, Cambridge.
416. [1914] NORBERT WIENER, A simplification of the logic of relations, Proceedings of the Cambridge Philosophical Society, vol. 17, pp. 387-390, reprinted in van Heijenoort [1967], pp. 224-227.
417. [1914] NORBERT WIENER, A simplification of the logic of relations, Proceedings of the Cambridge Philosophical Society, vol. 17, pp. 387-390, reprinted in van Heijenoort [1967], pp. 224-227.
418. [1956] LUDWIG WITTGENSTEIN, Remarks on the foundations of mathematics, Basil Blackwell, Oxford, edited by Georg H. von Wright, Rush Rhees and G. Elizabeth M. Anscombe, second printing, 1967.
419. [1904] ERNST ZERMELO, Beweis, dass jede Menge wohlgeordnet werden kann (Aus einem an Herrn Hilbert gerichteten Briefe), Mathematische Annalen, vol. 59, pp. 514-516, translated in van Heijenoort [1967], pp. 139-141.
420. [1904] ERNST ZERMELO, Beweis, dass jede Menge wohlgeordnet werden kann (Aus einem an Herrn Hilbert gerichteten Briefe), Mathematische Annalen, vol. 59, pp. 514-516, translated in van Heijenoort [1967], pp. 139-141.
421. [1908] _, Neuer Beweis für die Möglichkeit einer Wohlordnung, Mathematische Annalen, vol. 65, pp. 107-128, translated in van Heijenoort [1967], pp. 183-198.
422. [1908] _, Neuer Beweis für die Möglichkeit einer Wohlordnung, Mathematische Annalen, vol. 65, pp. 107-128, translated in van Heijenoort [1967], pp. 183-198.
423. [1908a] _, Untersuchungen über die Grundlagen der Mengenlehre I, Mathematische Annalen, vol. 65, pp. 261-281, translated in van Heijenoort [1967], pp. 199-215.
424. [1908a] _, Untersuchungen über die Grundlagen der Mengenlehre I, Mathematische Annalen, vol. 65, pp. 261-281, translated in van Heijenoort [1967], pp. 199-215.
425. [1929] _, Über den Begriff der Definitheit in der Axiomatik, Fundamenta Mathematicae, vol. 14, pp. 339-344.
426. [1930] _, Über Grenzzahlen und Mengenbereiche: Neue Untersuchungen über die Grundlagen der Mengenlehre, Fundamenta Mathematicae, vol. 16, pp. 29-47.
427. [1931] _, Über Stufen der Quantifikation und die Logik des Unendlichen, Jahresbericht der Deutschen Mathematiker-Vereinigung, vol. 41, pp. 85-88.
428. [1935] _, Grundlagen einer allgemeinen Theorie der mathematicschen Satzsysteme, Fundamenta Mathematicae, vol. 25, pp. 136-146.
429. [1935] MAX ZORN, A remark on method in transfinite algebra, Bulletin of the American Mathematical Society, vol. 41, pp. 667-670.