Axioms of infinity of set theory

Gaisi TAKEUTI

doi:10.2969/jmsj/01330220

Gaisi TAKEUTI

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1961 Volume 13 Issue 3 Pages 220-233

DOI https://doi.org/10.2969/jmsj/01330220

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Published: 1961 Received: March 07, 1960 Available on J-STAGE: August 29, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: August 29, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) K. Gödel, The consistency of the axiom of choice and of the gendralized continuum-hypothesis with the axioms of set theory, Revised ed., Princeton, 1951.
2) K. Gödel, Über formal unentscheidbare Sätze der Principia Mathematica und verwandter System I, Monatsh. Math. Ph., 38 (1930), 173-198.
3) A. Lévy, Contributions to the metamathematics of set theory, (Hebrew with English summary) 1958, Thesis, Hebrew University, Jerusalem.
4) A. Lévy, Axiom schemata of strong infinity in axiomatic set theory, Pacific J. Math., 10 (1960), 223-238.
5) P. Mahlo, Über lineare transfinite Mengen, Ber. Leipzig, 63 (1911), 187-225.
6) P. Mahlo, Zur Theorie und Anwendung der ρ0-Zahlen, Ber. Leipzig, 64 (1912), 108-112 65 (1913), 268-282.
7) J. B. Rosser, Extensions of some theorems of Gödel und Church, J.S.L., 1 (1936) 87-91.
8) J. C. Shepherdson, Inner models for set theory, J.S.L., (1951), 161-190; (1952), 225-237.
9) K. Schütte, Beweistheoritische Erfassung der unendlichen Induktion in der Zahlen Theorie, Math. Ann., 122 (1951). 369-389.
10) G. Takeuti, A metamathematical theorem on functions, J. Math. Soc. Japan, 8 (1956), 65-78.
11) G. Takeuti, Remark on the truth definition, J. Math. Soc. Japan, 13 (1961), 207-209.
12) A. Tarski, Der Wahrheitsbegriff in den formalisierten Sprachen, Studia Philos., 1 (1936), 26-405.
13) A. Tarski, Über unerreichbare Kardinalzahlen, Fund. Math., 30 (1938), 68-89.
14) A. Tarski, A. Mostowski and R. M. Robinson, Undecidable Theories, Amsterdam, 1953.

Right : [1] K. Gödel, The consistency of the axiom of choice and of the gendralized continuum-hypothesis with the axioms of set theory, Revised ed., Princeton, 1951.
[2] K. Gödel, Über formal unentscheidbare Sätze der Principia Mathematica und verwandter System I, Monatsh. Math. Ph., 38 (1930), 173-198.
[3] A. Lévy, Contributions to the metamathematics of set theory, (Hebrew with English summary) 1958, Thesis, Hebrew University, Jerusalem.
[4] A. Lévy, Axiom schemata of strong infinity in axiomatic set theory, Pacific J. Math., 10 (1960), 223-238.
[5] P. Mahlo, Über lineare transfinite Mengen, Ber. Leipzig, 63 (1911), 187-225.
[6] P. Mahlo, Zur Theorie und Anwendung der _ρ0-Zahlen, Ber. Leipzig, 64 (1912), 108-112; 65 (1913), 268-282.
[7] J. B. Rosser, Extensions of some theorems of Gödel und Church, J.S.L., 1 (1936) 87-91.
[8] J. C. Shepherdson, Inner models for set theory, J. S. L., (1951), 161-190; (1952), 225-237.
[9] K. Schütte, Beweistheoritische Erfassung der unendlichen Induktion in der Zahlen Theorie, Math. Ann., 122 (1951). 369-389.
[10] G. Takeuti, A metamathematical theorem on functions, J. Math. Soc. Japan, 8 (1956), 65-78.
[11] G. Takeuti, Remark on the truth definition, J. Math. Soc. Japan, 13 (1961), 207-209.
[12] A. Tarski, Der Wahrheitsbegriff in den formalisierten Sprachen, Studia Philos., 1 (1936), 26-405.
[13] A. Tarski, Über unerreichbare Kardinalzahlen, Fund. Math., 30 (1938), 68-89.
[14] A. Tarski, A. Mostowski and R. M. Robinson, Undecidable Theories, Amsterdam, 1953.

Date of correction: August 29, 2006 Reason for correction: - Correction: PDF FILE Details: -

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