Tarski's system of geometry

Bulletin of Symbolic Logic

Volumn 5, Issue 2, 1999, Pages 175-214

  Tarski, Alfred ^a   Givant, Steven ^a  

^a MILLS COLLEGE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033444539     PISSN: 10798986     EISSN: None     Source Type: Journal    
DOI: 10.2307/421089     Document Type: Article

References (57)

1. J. BOLYAI, Appendix scientiam spatii absolute veram exhibens: a veritate aut falsitate Axiomatis XI Euclidei (a priori haud unquam decidenda) independentem; adjecta ad casum falsitatis, quadratura circuit gcometrica, in F. BOLYAI, Tentamen juventutem studiosam in elementa matheseos purae, elementaris ac sublimioris methodo intuitiva, evidentiaque huic propria, introducendi. Cum Appendice triplici, vol. 1, Maros-Vásárhelyini, 1832, German translation in F. Engel and P. Stäckel, Urkunden zur Geschichte der nichteuklidischen Geometrie, Band 2, Teil 1, 2, B.G. Teubner, Leipzig and Berlin, 1913.
2. J. BOLYAI, Appendix scientiam spatii absolute veram exhibens: a veritate aut falsitate Axiomatis XI Euclidei (a priori haud unquam decidenda) independentem; adjecta ad casum falsitatis, quadratura circuit gcometrica, in F. BOLYAI, Tentamen juventutem studiosam in elementa matheseos purae, elementaris ac sublimioris methodo intuitiva, evidentiaque huic propria, introducendi. Cum Appendice triplici, vol. 1, Maros-Vásárhelyini, 1832, German translation in F. Engel and P. Stäckel, Urkunden zur Geschichte der nichteuklidischen Geometrie, Band 2, Teil 1, 2, B.G. Teubner, Leipzig and Berlin, 1913.
3. R. DEDEKIND, Stetigkeit und irrationale Zahlen, F. Vieweg, Braunschweig, 1872, 24 pp.
4. F. ENRIQUES, Fragen der Elementargeometrie, B.G. Teubner Verlag, Berlin and Leipzig, 1911.
5. M. GROCHOWSKA, Euclidean two dimensional equidistance theory, Demonstratio Mathematica, vol. 17 (1984), pp. 593-607.
6. H. N. GUPTA, Contributions to the axiomatic foundations of geometry, Doctoral dissertation, University of California, Berkeley, 1965, 407 pp.
7. M. KORDOS, On the syntactic form of dimension axiom for affine geometry, Bulletin de l'Academie Polonaise des Sciences, Série des Sciences Mathématiques, Astronomiques et Physiques, vol. 17 (1969), pp. 833-837.
8. _, Szkolna realizacja geometrii jako teorii opartej na aksjomatyce Szmielew i Tarskiego, Wiadomości Matematyczne, vol. 13 (1971), pp. 97-102.
9. A. M. LEGENDRE, Réflexions sur différentes manières de démontrer la théorie des parallèles, Memoires de l'académie royale des sciences de l'institut de France, vol. 12 (1833), pp. 367-410.
10. A. LINDENBAUM and A. TARSKI, Sur l'indépendance des notions primitives dans les systèmes mathématiques, Rocznik Polskiego Towarzystwa Matematycznego (=Annales de la Société Polonaise de Mathématique), vol. 5 (1927), pp. 111-113.
11. J. F. LORENZ, Grundriss der reinen und angewandten Mathematik, vol. I, C.G. Fleckeisen, Helmsted, 1791-92.
12. H. MAKOWIECKA, The theory of bi-proportionality as a geometry, Bulletin de l'Academie Polonaise des Sciences, Série des Sciences Mathématiques, Astronomiques et Physiques, vol. 23 (1975), pp. 657-664.
13. _, An elementary geometry in connection with decompositions of a plane, Bulletin de l'Academie Polonaise des Sciences, Série des Sciences Mathématiques, Astronomiques et Physiques, vol. 23 (1975), pp. 665-674.
14. _, On primitive notions in n-dimensional elementary geometries, Bulletin de l'Academie Polonaise des Sciences, Série des Sciences Mathématiques, Astronomiques et Physiques, vol. 23 (1975), pp. 675-682.
15. _, A general property of ternary relations in elementary geometry, Bulletin de l'Academie Polonaise des Sciences, Série des Sciences Mathématiques, Astronomiques et Physiques, vol. 24 (1976), pp. 163-169.
16. _, On minimal systems of primitives in elementary Euclidean geometry, Bulletin de l'Academie Polonaise des Sciences, Série des Sciences Mathématiques, Astronomiques et Physiques, vol. 25 (1977), pp. 269-277.
17. J. MOLLERUP, Die Beweise der ebenen Geometrie ohne Benutzung der Gleichheit und Ungleichheit der Winkel, Mathematische Annalen, vol. 58 (1903), pp. 479-496.
18. E. H. MOORE, On the projective axioms of geometry, Transactions of the American Mathematical Society, vol. 3 (1902), pp. 142-158.
19. M. MOSZYŃSKA, Review of Schwabhäuser-Szmielew-Tarski [29], this JOURNAL, vol. 51 (1986), pp. 1073-1075.
20. J. MYCIELSKI and S. ŚWIERCZKOWSKI, On the Lebesgue measurability and the axiom of determinateness, Fundamenta Mathematicae, vol. 54 (1964), pp. 67-71.
21. V. PAMBUCCIAN, Simple axiom systems for Euclidean geometry, Mathematical Chronicle, vol. 18 (1989), pp. 63-74.
22. _, On the simplicity of an axiom system for plane Euclidean geometry, Demonstratio Mathematica, vol. 30 (1997), pp. 509-512.
23. M. PASCH, Vorlesungen über neuere Geometrie, B.G. Teubner, Leipzig, 1882, 201 pp.
24. M. PIERI, La geometria elementare istituita sulle nozioni 'punto' é 'sfera', Memorie di Matematica e di Fisica della Società Italiana delle Scienze, vol. 15 (1908), pp. 345-450.
25. G. RICHTER and R. SCHNABEL, Euklidische Räume, Journal of Geometry, vol. 58 (1997), pp. 164-178.
26. R. M. ROBINSON, Binary relations as primitive notions in elementary geometry, The axiomatic method, with special reference to geometry and physics (L. Henkin, P. Suppes, and A. Tarski, editors), North-Holland Publishing Company, Amsterdam, 1959, pp. 68-85.
27. G. SACCHERI, Euclides ab omnis naevo vindicatus: sive conatus geometricus quo stabiliuntur prima ipsa universae geometricae principia, Paolo Antonio Montano, Milano, 1733.
28. R. SCHNABEL, Euklidische Geometrie, Habilitation, Kiel, 1978, iii+111 pp.
29. F. SCHUR, Grundlagen der Geometrie, B.G. Teubner Verlag, Berlin and Liepzig, 1909, x+192 pp.
30. W. SCHWABHÄUSER, W. SZMIELEW, and A. TARSKI, Metamathematische Methoden in der Geometrie, Hochschultext, Springer-Verlag, Berlin, 1983, viii+483 pp.
31. D. SCOTT, Dimension in elementary Euclidean geometry, The axiomatic method, with special reference to geometry and physics (L. Henkin, P. Suppes, and A. Tarski, editors), North-Holland Publishing Company, Amsterdam, 1959, pp. 53-67.
32. W. SIERPIŃSKI, Cardinal and ordinal numbers, Państwowe Wydawnictwo Naukowe, Warszawa, 1958, 491 pp.
33. R. M. SOLOVAY, A model of set theory in which every set of reals is Lebesgue measurable, Annals of Mathematics, vol. 92, (1970), pp. 1-56.
34. L. W. SZCZERBA, Independence of Pasch's axiom, Bulletin de l'Academie Polonaise des Sciences, Série des Sciences Mathématiques, Astronomiques et Physiques, vol. 18 (1970), pp. 491-498.
35. L. W. SZCZERBA and A. TARSKI, Metamathematical properties of some affine geometries, Proceedings of the 1964 International Congress for Logic, Methodology and Philosophy of Science (Y. Bar-Hillel, editor), Studies in Logic and the Foundations of Mathematics, North-Holland Publishing Company, Amsterdam, 1965, pp. 166-178.
36. _, Metamathematical discussion of some affine geometries, Fundamenta Mathematicae, vol. 104 (1979), pp. 155-192.
37. W. SZMIELEW, Elementary properties of Abelian groups, Fundamenta Mathematicae, vol. 41 (1955), pp. 203-271.
38. _, Some metamathematical problems concerning elementary hyperbolic geometry, The axiomatic method, with special reference to geometry and physics (L. Henkin, P. Suppes, and A. Tarski, editors), North-Holland Publishing Company, Amsterdam, 1959, pp. 30-52.
39. _, From affine to Euclidean geometry: An axiomatic approach, translated by M. Moszyńska, PWN-Polish Scientific Publishers, Warszawa, and D. Reidel Publishing Company, Dordrecht, 1983, xiii+194 pp.; this is an English Translation of Od geometrii affinicznej do Euklidesowej - Rozwżania nad aksjomatyka̧, edited and prepared for publication by M. Moszyńska, Państwowe Wydawnictwo Naukowe, Warszawa, 1981, 172 pp.
40. _, From affine to Euclidean geometry: An axiomatic approach, translated by M. Moszyńska, PWN-Polish Scientific Publishers, Warszawa, and D. Reidel Publishing Company, Dordrecht, 1983, xiii+194 pp.; this is an English Translation of Od geometrii affinicznej do Euklidesowej - Rozwżania nad aksjomatyka̧, edited and prepared for publication by M. Moszyńska, Państwowe Wydawnictwo Naukowe, Warszawa, 1981, 172 pp.
41. A. TARSKI, Sur les ensembles définissables de nombres réels, I, Fundamenta Mathematicae, vol. 17 (1931), pp. 210-239; an English translation appeared as Article VI in [43].
42. _, Einige methodologische Untersuchungen über die Definierbarkeit der Begriffe, Erkenntnis, vol. 5 (1935), pp. 80-100; this is a German translation of Z badań metodologicznych nad definjowalnościǎ terminów, Przegla̧d Filozoficzny (=Revue Philosophique), vol. 37 (1934), pp. 438-460; an English translation appear as Article X in Tarski [43].
43. _, Einige methodologische Untersuchungen über die Definierbarkeit der Begriffe, Erkenntnis, vol. 5 (1935), pp. 80-100; this is a German translation of Z badań metodologicznych nad definjowalnościǎ terminów, Przegla̧d Filozoficzny (=Revue Philosophique), vol. 37 (1934), pp. 438-460; an English translation appear as Article X in Tarski [43].
44. _, A decission method for elementary algebra and geometry, prepared for publication by J. C. C. McKinsey, U.S. Air Force Project RAND, R-109, the RAND Corporation, Santa Monica, 1948, iv+60 pp.; a second, revised edition was published by the University of California Press, Berkeley and Los Angeles, CA, 1951, iii+63 pp.
45. _, A general theorem concerning primitive notions of Euclideans geometry, Indagationes Mathematicae, vol. 18 (= Koninklijkle Nederlandse Akademie van Wetenschappen, Proceedings, Series A, Mathematical Sciences, vol. 59) (1956), pp. 468-474.
46. _, Logic, semantics, metamathematics: Papers from 1923 to 1938 (translated by J. H. Woodger), Clarendon Press, Oxford, 1956, xiv+471 pp.
47. _, What is elementary geometry?, The axiomatic method, with special reference to geometry and physics (L. Henkin, P. Suppes, and A. Tarski, editors), North-Holland Publishing Company, Amsterdam, 1959, pp. 16-29.
48. _, The completeness of elementary algebra and geometry, Institut Blaise Pascal, Paris, 1967, iv+50 pp.
49. _, Alfred Tarski: Collected papers (S. R. Givant and R. N. McKenzie, editors), Birkhäuser, Basel, 1986, vol. 1, xvi+659 pp.; vol. 2, xvi+69 pp.; vol. 3, xvi+682 pp.; vol. 4, xvi+757 pp.
50. _, Alfred Tarski: Collected papers (S. R. Givant and R. N. McKenzie, editors), Birkhäuser, Basel, 1986, vol. 1, xvi+659 pp.; vol. 2, xvi+69 pp.; vol. 3, xvi+682 pp.; vol. 4, xvi+757 pp.
51. _, Alfred Tarski: Collected papers (S. R. Givant and R. N. McKenzie, editors), Birkhäuser, Basel, 1986, vol. 1, xvi+659 pp.; vol. 2, xvi+69 pp.; vol. 3, xvi+682 pp.; vol. 4, xvi+757 pp.
52. _, Alfred Tarski: Collected papers (S. R. Givant and R. N. McKenzie, editors), Birkhäuser, Basel, 1986, vol. 1, xvi+659 pp.; vol. 2, xvi+69 pp.; vol. 3, xvi+682 pp.; vol. 4, xvi+757 pp.
53. A. TARSKI, N. FELDMAN, T. GREEN, W. HANF, L. HENKIN, S. ISARD, and A. KOSTINSKY, Basic research in the foundations of mathematics, Report for the period July 1, 1964-June 30, 1968 of a project supported by National Science Foundation Grants GP-1395, GP-4608, and GP-6232X, Department of Mathematics, University of California, Berkeley, CA, mimeograph, 1970, ii+53 pp.
54. A. TARSKI, H. GAIFMAN, and A. LÉVY, Basic research in the foundations of mathematics, Report for the period July 1, 1959-June 30, 1961 of a project supported by National Science Foundation Grants G6693 and G14006, Department of Mathematics, University of California, Berkeley, CA, mimeograph, 1962, 33 pp.
55. A. TARSKI, L. HENKIN, and W. RUPLEY, Basic research in the foundations of mathematics, Report for the period July 1, 1961-June 30, 1964 of a project supported by National Science Foundation Grants G6693, G14006, G19673, and GP-1395, Department of Mathematics, University of California, Berkeley, CA, mimeograph, 1965, 80 pp.
56. O. VEBLEN, A system of axioms for geometry, Transactions of the American Mathematical Society, vol. 5 (1904), pp. 343-384.
57. _, The foundations of geometry, Monographs on topics of modern mathematics, relevant to the elementary field (J. W. A. Young, editor), Longsman, Green, and Company, New York, 1914, pp. 1-51.