Hilbert's Program then and Now

Philosophy of Logic

Volumn , Issue , 2007, Pages 411-447

  Zach, Richard ^a  

^a UNIVERSITY OF CALGARY   (Canada)

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EID: 72749104691     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1016/B978-044451541-4/50014-2     Document Type: Chapter

References (151)

1. Ackermann W. Begründung des "tertium non datur" mittels der Hilbertschen Theorie der Widerspruchsfreiheit. Mathematische Annalen 1925, 93:1-36.
2. Ackermann W. Zur Widerspruchsfreiheit der Zahlentheorie. Mathematische Annalen 1940, 117:162-194.
3. Arai T. Derivability conditions on Rosser's provability predicates. Notre Dame Journal of Formal Logic 1990, 31:487-497.
4. 1({fx442-01). Annals of Pure and Applied Logic 2003, 121:163-208.
5. Auerbach D. Intentionality and the Gödel theorems. Philosophical Studies 1985, 48:337-351.
6. Auerbach D. How to say things with formalisms. Proof, Logic, and Formalization 1992, 77-93. Routledge, London. M. Detlefsen (Ed.).
7. Avigad J. Number theory and elementary arithmetic. Philosophia Mathematica 2003, 11:257-284.
8. Avigad J., Feferman S. Gödel's functional ("Dialectica") interpretation 1998, In Buss.
9. Avigad J., Reck E. Clarifying the nature of the infinite": the development of metamathematics and proof theory. Technical report cmu-phil-120 2001, Online at, Carnegie Mellon University. http://www.andrew.cmu.edu/user/avigad/Papers/infinite.pdf.
10. Avigad J., Zach R. The epsilon calculus. The Stanford Encyclopedia of Philosophy 2002, Summer. http://www.plato.stanford.edu/entries/epsiloncalculus, E. N. Zalta (Ed.).
11. Handbook of Mathematical Logic 1977, North-Holland, Amsterdam. J. Barwise (Ed.).
12. Philosophy of Mathematics 1983, Cambridge University Press, Cambridge. 2nd edition. P. Benacerraf, H. Putnam (Eds.).
13. Bernays P. über Hilberts Gedanken zur Grundlegung der Arithmetik. Jahresbericht der Deutschen Mathematiker-Vereinigung 1922, 31:10-19. English translation in [Mancosu, 1998a, 215-222].
14. Bernays P. Erwiderung auf die Note von Herrn Aloys Müller: über Zahlen als Zeichen. Mathematische Annalen 1923, 90:59-63. English translation in [Mancosu, 1998a, 223-226].
15. Bernays P. über Nelsons Stellungnahme in der Philosophie der Mathematik. Die Naturwissenschaften 1928, 16:42-45.
16. Bernays P. Zusatz zu Hilberts Vortrag über "Die Grundlagen der Mathematik". Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1928, 6:88-92. English translation in: [van Heijenoort, 1967, 485-489].
17. Bernays P. Die Philosophie der Mathematik und die Hilbertsche Beweistheorie. Blätter für deutsche Philosophie 1930, 4:32-67. Reprinted in [Bernays, 1976, 17-61]. English translation in [Mancosu, 1998a, 234-265].
18. Bernays P. On the original Gentzen consistency proof. Intuitionism and Proof Theory 1970, 409-417. North-Holland, Amsterdam. A. Kino, J. Myhill, R.E. Veseley (Eds.).
19. Bernays P. Abhandlungen zur Philosophie der Mathematik 1976, Wissenschaftliche Buchgesellschaft, Darmstadt.
20. Handbook of Proof Theory 1998, Elsevier, Amsterdam. S.R. Buss (Ed.).
21. Caldon P., Ignjatovič A. On mathematical instrumentalism. Journal of Symbolic Logic 2005, 70:778-794.
22. Detlefsen M. On interpreting Gödel's second theorem. Journal of Philosophical Logic 1979, 8:297-313. Reprinted with a postscript in [Shanker, 1988, 131-154].
23. Detlefsen M. Hilbert's Program 1986, Reidel, Dordrecht.
24. Detlefsen M. On an alleged refutation of Hilbert's program using Gödel's first incompleteness theorem. Journal of Philosophial Logic 1990, 19:343-377.
25. Detlefsen M. What does Gödel's second theorem say?. Philosophia Mathematica 2001, 9:37-71.
26. Detlefsen M. Formalism. The Oxford Handbook of Philosophy of Mathematics and Logic 2005, 236-317. Oxford University Press, New York and Oxford. S. Shapiro (Ed.).
27. From Kant to Hilbert. A Source Book in the Foundations of Mathematics 1996, volume 2. Oxford University Press, Oxford. W.B. Ewald (Ed.).
28. Feferman S. Arithmetization of metamathematics in a general setting. Fundamenta Mathematicae 1960, 35-92.
29. Feferman S. Hilbert's Program relativized: Proof-theoretical and foundational reductions. Journal of Symbolic Logic 1988, 53(2):64-284.
30. Feferman S. What rests on what? The proof-theoretic analysis of mathematics. Philosophy of Mathematics. Proceedings of the Fifteenth International Wittgenstein-Symposium, Part 1 1993, 147-171. Vienna, Hölder-Pichler- Tempsky. Reprinted in [Feferman, 1998, Ch. 10, 187-208]. J. Czermak (Ed.).
31. Feferman S. Why a little bit goes a long way: Logical foundations of scienti .cally applicable mathematics. Proceedings of the Philosophy of Science Association 1992 1993, 2:442-455. Reprinted in [Feferman, 1998, Ch. 14, 284-298].
32. Feferman S. In the Light of Logic 1998, Oxford University Press, New York and Oxford.
33. Feferman Solomon Does reductive proof theory have a viable rationale?. Erkenntnis 2000, 53:63-96.
34. Field H. Science without Numbers. A Defence of Nominalism 1980, Princeton University Press, Princeton.
35. Gentzen G. über das Verhältnis zwischen intuitionistischer und klassischer Logik. First published in Archiv für mathematische Logik und Grundlagenforschung 1974, 16:119-132. English translation in [Gentzen, 1969, 53-67], 1933.
36. Gentzen G. Untersuchungen über das logische Schließen I-II. Mathematische Zeitschrift 1934, 39:176-210. English translation in [Gentzen, 1969, 68-131].
37. Gentzen G. Untersuchungen über das logische Schließen I-II. Mathematische Zeitschrift 1934, 39:405-431. English translation in [Gentzen, 1969, 68-131].
38. Gentzen G. Die Widerspruchsfreiheit der reinen Zahlentheorie. Published as "Der erste Widerspruchsfreiheitsbeweis für die klassische Zahlentheorie" in Archiv für mathematische Logik und Grundlagenforschung 1974, 16:97-118. English translation in [Gentzen, 1969, 132-213], 1935.
39. Gentzen G. Die Widerspruchsfreiheit der reinen Zahlentheorie. Mathematische Annalen 1936, 112:493-565. English translation in [Gentzen, 1969, 132-213].
40. Gentzen G. Beweisbarkeit und Unbeweisbarkeit von Anfangsfällen der trans- .niten Induktion in der reinen Zahlentheorie. Mathematische Annalen 1943, 119:140-161. English translation in [Gentzen, 1969, 287-308].
41. Gentzen G. The Collected Papers of Gerhard Gentzen 1969, North-Holland, Amsterdam. M.E. Szabo (Ed.).
42. Giaquinto M. Hilbert's philosophy of mathematics. British Journal for Philosophy of Science 1983, 34:119-132.
43. Gödel K. über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I. Monatshefte für Mathematik und Physik 1931, 38:173-198. Reprinted and translated in [Gödel, 1986, 144-195].
44. Gödel K. Zur intuitionistischen Arithmetik und Zahlentheorie. Ergebnisse eines mathematisches Kolloquiums 1933, 4:34-38. Reprinted and translated in [Gödel, 1986, 286- 295].
45. Gödel K. über eine bisher noch nicht benütze Erweiterung des .niten Standpunktes. Dialectica 1958, 280-287. Reprinted and translated in [Gödel, 1995, 217-251].
46. Gödel K. Collected Works 1986, volume 1. Oxford University Press, Oxford. S. Feferman (Ed.).
47. Gödel K. Collected Works 1995, volume 2. Oxford University Press, Oxford. S. Feferman (Ed.).
48. Gödel K. Collected Works 2003, volume 4. Oxford University Press, Oxford. S. Feferman (Ed.).
49. Gödel K. Collected Works 2003, volume 5. Oxford University Press, Oxford. S. Feferman (Ed.).
50. Guaspari D., Solovay R.M. Rosser sentences. Annals of Mathematical Logic 1979, 16:81-99.
51. Hallett M. Physicalism, reductionism and Hilbert. Physicalism in Mathemtics 1990, 183-257. Reidel, Dordrecht. A. D. Irvine (Ed.).
52. Hallett M. Hilbert's axiomatic method and the laws of thought. Mathematics and Mind 1994, 158-200. Oxford University Press, Oxford. A. George (Ed.).
53. Herbrand J. Recherches sur la théorie de la démonstration. Doctoral dissertation 1930, English translation in [Herbrand, 1971, 44-202], University of Paris.
54. Herbrand J. Logical Writings 1971, Harvard University Press. W. D. Goldfarb (Ed.).
55. Hilbert D. Grundlagen der Geometrie. Festschrift zur Feier der Enthüllung des Gauss-Weber-Denkmals in Göttingen 1899, 1-92. reprinted in [Hilbert, 2004], Teubner, Leipzig. 1st edition.
56. Hilbert D. Mathematische Probleme. Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen, Math.-Phys. Klasse 1900, 253-297. 1900. Partial English translation in [Ewald, 1996, 1096-1105], Lecture given at the International Congress of Mathematicians, Paris.
57. Hilbert D. über den Zahlbegri. Jahresbericht der Deutschen Mathematiker- Vereinigung 1900, 8:80-84. English translation in [Ewald, 1996, 1089-1096].
58. Hilbert D. über die Grundlagen der Logik und der Arithmetik. Verhandlungen des dritten Internationalen Mathematiker-Kongresses in Heidelberg vom 8. bis 13. August 1904 1905, 74-85. Leipzig, Teubner. English translation in [van Heijenoort, 1967, 129-38]. A. Krazer (Ed.).
59. Hilbert D. Axiomatisches Denken. Mathematische Annalen 1918, 78:5-15. Lecture given at the Swiss Society of Mathematicians, 11 September 1917. Reprinted in [Hilbert, 1935, 146-56]. English translation in [Ewald, 1996, 1105-1115].
60. Hilbert D. Prinzipien der Mathematik. Lecture notes by Paul Bernays. Winter- Semester 1917-18 1918, Unpublished typescript, Published in [Hilbert, 2006], Bibliothek, Mathematisches Institut, Universität Göttingen.
61. Hilbert D. Probleme der mathematischen Logik. Sommer-Semester. Sommer-Semester. Sommer-Semester 1920, Lecture notes by Paul Bernays and Moses Schönfinkel. Unpublished typescript. Bibliothek, Mathematisches Institut, Universität Göttingen, Vorlesung, Mathematisches Institut, Universität Göttingen, Vorlesung, Mathematisches Institut, Universität Göttingen, Vorlesung, Published in. Hilbert (Ed.), Hilbert (Ed.).
62. Hilbert D. Grundlagen der Mathematik. Vorlesung, Winter-Semester 1921-22 1922, Lecture notes by Paul Bernays. Unpublished typescript, Published in [Hilbert, 2006], Bibliothek, Mathematisches Institut, Universität Göttingen.
63. Hilbert D. Neubegründung der Mathematik: Erste Mitteilung. Abhandlungen aus dem Seminar der Hamburgischen Universität 1921, 1:57-77. July 25-27, Series of talks given at the University of Hamburg, Reprinted with notes by Bernays in [Hilbert, 1935, 157-177]. English translation in [Mancosu, 1998a, 198-214] and [Ewald, 1996, 1115-1134].
64. Hilbert D. Die logischen Grundlagen der Mathematik. Mathematische Annalen 1923, 88:151-165. Lecture given at the Deutsche Naturforscher-Gesellschaft, September 1922. Reprinted in [Hilbert, 1935, 178-191]. English translation in [Ewald, 1996, 1134-114.
65. Hilbert D. über das Unendliche. Mathematische Annalen 1926, 95:61-90. Lecture given Münster, 4 June 1925. English translation in [van Heijenoort, 1967, 367-392].
66. Hilbert D. Die Grundlagen der Mathematik. Abhandlungen aus dem Seminar der Hamburgischen Universität 1928, 6:65-85. English translation in [van Heijenoort, 1967, 464-479].
67. Hilbert D. Probleme der Grundlegung der Mathematik. Mathematische Annalen 1929, 102:1-9. Lecture given at the International Congress of Mathematicians, 3 September 1928. English translation in [Mancosu, 1998a, 227-233].
68. Hilbert D. Beweis des Tertium non datur. Nachrichten der Gesellschaft der Wissenschaften zu Göttingen. Math.-phys. Klasse 1931, 20-25.
69. Hilbert D. Die Grundlegung der elementaren Zahlenlehre. Mathematische Annalen 1931, 104:85-94. Reprinted in [Hilbert, 1935, 192-195]. English translation in [Ewald, 1996, 1148-1157].
70. Hilbert D. Gesammelte Abhandlungen 1935, volume 3. Springer, Berlin.
71. Hilbert D. Natur und mathematisches Erkennen 1992, Vorlesungen, 1919-20, Birkhäuser, Basel.
72. Hilbert D. David Hilbert's Lectures on the Foundations of Geometry, 1891- 1902 2004, Springer, New York. U. Majer, M. Hallett (Eds.).
73. Hilbert D. David Hilbert's Lectures on the Foundations of Arithmetic and Logic, 1917-1933 2006, forthcoming, Springer, New York. W. Ewald, W. Sieg (Eds.).
74. Hilbert D., Ackermann W. Grundzüge der theoretischen Logik 1928, Springer, Berlin.
75. Hilbert D., Bernays P. Logische Grundlagen der Mathematik. Vorlesung, Winter-Semester 1922-23 1923, Lecture notes by Paul Bernays, with handwritten notes by Hilbert, Published in [Hilbert, 2006], Hilbert-Nachlaß, Niedersächsische Staats- und Universitätsbibliothek, Cod. Ms. Hilbert 567.
76. Hilbert D., Bernays P. Grundlagen der Mathematik 1934, volume 1. Springer, Berlin.
77. Hilbert D., Bernays P. Grundlagen der Mathematik 1939, volume 2. Springer, Berlin.
78. Hofweber T. Proof-theoretic reduction as a philosopher's tool. Erkenntnis 2000, 53:127-146.
79. Ignjatovič A. Hilbert's program and the omega-rule. Journal of Symbolic Logic 1994, 59:322-343.
80. Jeroslow R.G. Consistency statements in formal theories. Fundamenta Mathematicae 1971, 72:17-40.
81. Jeroslow R.G. Experimental logics and .0 2-theories. Journal of Philosophical Logic 1975, 4:253-267.
82. Kitcher P. Hilbert's epistemology. Philosophy of Science 1976, 43:99-115.
83. Kreisel G. On the interpretation of non-finitist proofs. Part I. Journal of Symbolic Logic 1951, 16:241-267.
84. Kreisel G. A variant to Hilbert's theory of the foundations of arithmetic. British Journal for the Philosophy of Science 1954, 4:107-129.
85. Kreisel G. Ordinal logics and the characterization of informal notions of proof. Proceedings of the International Congress of Mathematicians. Edinburgh, 14-21 August 1958 1960, 289-299. Cambridge, Cambridge University Press. J.A. Todd (Ed.).
86. Kreisel G. A survey of proof theory. Journal of Symbolic Logic 1968, 33:321-388.
87. Kreisel G. Principles of proof and ordinals implicit in given concepts. Intuitionism and Proof Theory 1970, 489-516. North- Holland, Amsterdam. A. Kino, J. Myhill, R.E. Veseley (Eds.).
88. Kreisel G. Review of The Collected Papers of Gerhard Gentzen [Gentzen, 1969]. Journal of Philosophy 1971, 68:238-265.
89. Kreisel G. Wie die Beweistheorie zu ihren Ordinalzahlen kam und kommt. Jahresberichte der Deutschen Mathematiker-Vereinigung 1976, 78:177-223.
90. Kreisel G. Hilbert's programme. Benacerraf and Putnam 1983, 207-238.
91. Mancosu P., Ryckman T. Mathematics and phenomenology: The correspondence between O. Becker and H. Weyl. Philosophia Mathematica 2002, 10:130-202.
92. From Brouwer to Hilbert. The Debate on the Foundations of Mathematics in the 1920s 1998, Oxford University Press, Oxford. P. Mancosu (Ed.).
93. Mancosu P. Hilbert and Bernays on metamathematics. From Brouwer to Hilbert 1998, 149-188.
94. Mancosu P. Between Russell and Hilbert: Behmann on the foundations of mathematics. Bulletin of Symbolic Logic 1999, 5(3):303-330.
95. Mancosu P. The Russellian influence on Hilbert and his school. Synthèse 2003, 137(1-2):59-101.
96. Mancosu P. Review of Kurt Gödel. Collected Works 2003, vols. IV and V, Oxford University Press, Oxford. S. Feferman (Ed.).
97. Notre Dame Journal of Formal Logic 2004, 45:109-125.
98. Mints G., Tupailo S. Epsilon-substitution method for the rami .ed language and .1 1-comprehension rule. Logic and Foundations of Mathematics 1999, 107-130. Kluwer, Dordrecht. A. Cantini (Ed.).
99. Moore G.H. Hilbert and the emergence of modern mathematical logic. Theoria (Segunda época) 1997, 12:65-90.
100. Müller A. über Zahlen als Zeichen. Mathematische Annalen 1923, 90:153-158.
101. Müller A. über Zahlen als Zeichen. Mathematische Annalen 1923, 90:163.
102. Negri M. Constructive sequent reduction in Gentzen's first consistency proof for arithmetic. Italian Studies in the Philosophy of Science 1980, 153-168. Reidel, Dordrecht. M. Luisa Dalla Chiara (Ed.).
103. Paris J., Harrington L. A mathematical incompleteness in Peano arithmetic 1977, 1133-1142. Barwise (Ed.).
104. Parsons C. Finitism and intuitive knowledge. The Philosophy of Mathematics Today 1998, 249-270. Oxford University Press, Oxford. M. Schirn (Ed.).
105. Peckhaus V. Hilbertprogramm und Kritische Philosophie 1990, Vandenhoeck und Ruprecht, Göttingen.
106. Pohlers W. Contributions of the Schütte school school in Munich to proof theory 1987, Appendix to [Takeuti, 1987].
107. Pohlers W. Subsystems of set theory and second-order number theory 1998, Buss (Ed.).
108. Poincaré H. Les mathématiques et la logique. Revue de métaphysique et de morale 1906, 14:294-317. English translation in [Ewald, 1996, 1038-1052].
109. Pudlák P. The length of proofs 1998, Buss (Ed.).
110. Raatikainen Panu Hilbert's program revisited. Synthèse 2003, 137:157-177.
111. Ramsey F.P. Mathematical logic. The Mathematical Gazette 1926, 13:85-94. Reprinted in [Ramsey, 1990, 225-244].
112. Ramsey F.P. Philosophical Papers 1990, Cambridge University Press, Cambridge. D.H. Mellor (Ed.).
113. Rathjen M. An ordinal analysis of parameter free {fx446-02}-comprehension. Archive for Mathematical Logic 2005, 44:263-362.
114. Rathjen M. An ordinal analysis of stability. Archive for Mathematical Logic 2005, 44:1-62.
115. Resnik M.D. The Frege-Hilbert controversy. Philosophy and Phenomenological Research 1974, 34:386-403.
116. Resnik M.D. On the philosophical significance of consistency proofs. Journal of Philosophical Logic 1974, 3:33-47.
117. Resnik M.D. Frege and the Philosophy of Mathematics 1980, Cornell University Press, Ithaca.
118. Russell B. Letter to Frege 1902, 124-125. June 16, 1967. V. Heijenoort (Ed.).
119. Schütte K. Beweistheorie 1960, Springer, Berlin.
120. Shanker S.G. Gödel's Theorem in Focus 1988, Routledge, London.
121. Sieg W. Reflections on Hilbert's program. Acting and Reflecting 1990, 71-82. Kluwer, Dordrecht. W. Sieg (Ed.).
122. Sieg W. Hilbert's programs: 1917-1922. Bulletin of Symbolic Logic 1999, 5(1):1-44.
123. Sieg W. Beyond Hilbert's reach?. Reading Natural Philosophy. Essays in the History and Philosophy of Science and Mathematics 2002, 363-405. Open Court, Chicago and La Salle, Ill. D. B. Malament (Ed.).
124. Simpson S.G. Partial realizations of Hilbert's program. Journal of Symbolic Logic 1988, 53(2):349-363.
125. Simpson S.G. Subsystems of Seond Order Arithmetic 1999, Springer, Berlin.
126. Simpson S.G. Reverse Mathematics 2001. Lecture Notes in Logic 21 2005, Association for Symbolic Logic and A K Peters, Wellesley, Mass.
127. Smoryński C. The incompleteness theorems 1977, 821-865. Barwise (Ed.).
128. Stein Howard Logos, logic, and logisitiké: Some philosophical remarks on nineteenth-century transformation of mathematics. History and Philosophy of Modern Mathematics, volume 11 of Minesota Studies in the Philosophy of Science 1988, 238-259. University of Minnesota Press. W. Aspray, P. Kitcher (Eds.).
129. Steiner M. Mathematical Knowledge 1975, Cornell University Press, Ithaca.
130. Steiner M. Review of Hilbert's Program: An Essay on Mathematical Instrumentalism [Detlefsen, 1986]. Journal of Philosophy 1991, 88(6):331-336.
131. Tait W.W. Finitism. Journal of Philosophy 1981, 78:524-546. Reprinted in [Tait, 2005b, 21-42].
132. Tait W.W. Remarks on finitism. Lecture Notes in Logic 15 2002, Reprinted in [Tait, 2005b, 43-53], Association for Symbolic Logic and A K Peters. W. Sieg, R. Sommer, C. Talcott (Eds.).
133. Tait W.W. Gödel's reformulation of Gentzen's first consistency proof for arithmetic: the no-counterexample interpretation. Bulletin of Symbolic Logic 2005, 11:225-238.
134. Tait W.W. The Provenance of Pure Reason. Essays in the Philosophy of Mathematics and Its History 2005, Oxford University Press, New York.
135. Takeuti G. Proof Theory. Studies in Logic 81 1987, North-Holland, Amsterdam. 2nd edition.
136. From Frege to Gödel. A Source Book in Mathematical Logic, 1897-1931 1967, Harvard University Press, Cambridge, Mass. J. van Heijenoort (Ed.).
137. Visser A. Peano's smart children: A provability logical study of systems with built-in consistency. Notre Dame Journal of Formal Logic 1989, 30:161-196.
138. von Neumann J. Zur Hilbertschen Beweistheorie. Mathematische Zeitschrift 1927, 26:1-46.
139. von Neumann J. Die formalistische Grundlegung der Mathematik. Erkenntnis 1931, 2:16-34. English translation in: [Benacerraf and Putnam, 1983, 61-65].
140. Webb J.C. Hilbert's formalism and arithmetization of mathematics. Synthèse 1997, 110:1-14.
141. Weyl Hermann über die neue Grundlagenkrise der Mathematik. Mathematische Zeitschrift 1921, 10:37-79. Reprinted in [Weyl, 1968, 143-180]. English translation in [Mancosu, 1998a, 86-118].
142. Weyl H. Die heutige Erkenntnislage in der Mathematik. Symposion 1925, 1:1-23. Reprinted in: [Weyl, 1968, 511-42]. English translation in: [Mancosu, 1998a, 123-42].
143. Weyl H. Diskussionsbemerkungen zu dem zweiten Hilbertschen Vortrag über die Grundlagen der Mathematik. Abhandlungen aus dem Mathematischen Seminar der Universit ät Hamburg 1928, 6:86-88. English translation in [van Heijenoort, 1967, 480-484].
144. Weyl H. Gesammelte Abhandlungen 1968, volume 1. Springer Verlag, Berlin. K. Chandrasekharan (Ed.).
145. Whitehead A.N., Russell B. Principia Mathematica 1910, volume 1. Cambridge University Press, Cambridge.
146. Whitehead A.N., Russell B. Principia Mathematica 1912, volume 2. Cambridge University Press, Cambridge.
147. Whitehead A.N., Russell B. Principia Mathematica 1913, volume 3. Cambridge University Press, Cambridge.
148. Zach R. Completeness before Post: Bernays, Hilbert, and the development of propositional logic. Bulletin of Symbolic Logic 1999, 5(3):331-366.
149. Zach R. Hilbert's program. The Stanford Encyclopedia of Philosophy 2003, Fall. http://www.plato.stanford.edu/archives/entries/hilbertprogram, E. N. Zalta (Ed.).
150. Zach R. The practice of finitism. Epsilon calculus and consistency proofs in Hilbert's Program. Synthèse 2003, 137:211-259.
151. Zach R. Hilbert's "Verunglückter Beweis," the first epsilon theorem and consistency proofs. History and Philosophy of Logic 2004, 25:79-94.