Recursive progression of intuitionistic number theories

Reijiro KURATA

doi:10.2969/jmsj/01720140

Reijiro KURATA

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JOURNAL FREE ACCESS

1965 Volume 17 Issue 2 Pages 140-166

DOI https://doi.org/10.2969/jmsj/01720140

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Published: 1965 Received: January 06, 1964 Available on J-STAGE: September 26, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: September 26, 2006 Reason for correction: - Correction: DTRECEIVED Details: Wrong : 19640606
Right : 19640106

Date of correction: September 26, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) S. Feferman, Transfinite recursive progression of Axiomatic theories (1960), J. Symbolic Logic, 27 (1962), 259-316.
2) S. Kleene, Introduction to Metamathematics (1952), North Holland Publishing Co., Amsterdam.
3) M. Yasugi, Intuitionistic analysis and Gödel's interpretation. Reports, Symposium of Metamathematics at Tokyo Metropolitan University (1961).
4) M. Yasugi, Intuitionistic analysis and Gödel's interpretation, J. Math. Soc. Japan 15 (1963), 101-112.
5) K. Gödel, Über eine bisher noch nicht benützte Erweiterung des finiten Stand-punktes, Bibliothèque Scientifique 34, Logica (1960), 76-83.
6) G. Kreisel, Interpretation of analysis by means of constructive functionals of finite types, Constructivity in Mathematics, Amsterdam (1959), 101-128.
7) W. Craig, On axiomatizability with in a system, J. Symbolic Logic, 18 (1953), 30-32.
8) J. B. Rosser, Gödel theorems for non constructive logics, J. Symbolic Logic, 2 (1937), 129-137.
9) Hilbert Bernays, Grundlagen der Mathematik II.
10) S. Feferman, Arithmetization of metamathematics in a general setting, Fund. Math., 49 (1960), 35-92.
11) G. Gentzen, Beweisbarkeit und Unbeweisbarkeit von Anfangsfällen der transfiniten Induktion in der reinen Zahlentheorie, Math. Ann., 119 (1943), 140-161.
12) K. Gödel, Zur intuitionistischen Arithmetik und Zahlentheorie, Ergebnisse eines math. Koll., 4 (1932), 34-38.
13) T. Nishimura, On Gödel's theorem, J. Math. Soc. Japan, 13 (1961), 1-12.
14) T. Nishimura, Consistency and impredicative statements, Ann. Japan Assoc. Philos. Sci. 2 (1963), 14-26.
15) A. Mostowski, Some impredicative definitions in the axiomatic set-theory, Fund. Math., 37 (1950), 111-124.
16) H. Wang, Truth definitions and consistency proofs, Trans. Amer. Math. Soc., 73 (1952), 243-275.
17) G. Kreisel, On the interpretation of non finitist proofs part I, II, J. Symolic Logic, 16 (1951), 241-267 and 17 (1952), 43-58.

Right : [1] S. Feferman, Transfinite recursive progression of Axiomatic theories (1960), J. Symbolic Logic, 27 (1962), 259-316.
[2] S. Kleene, Introduction to Metamathematics (1952), North Holland Publishing Co., Amsterdam.
[3] M. Yasugi, Intuitionistic analysis and Gödel's interpretation. Reports, Symposium of Metamathematics at Tokyo Metropolitan University (1961).
[4] M. Yasugi, Intuitionistic analysis and Gödel's interpretation, J. Math. Soc. Japan 15 (1963), 101-112.
[5] K. Gödel, Über eine bisher noch nicht benützte Erweiterung des finiten Stand-punktes, Bibliothèque Scientifique 34, Logica (1960), 76-83.
[6] G. Kreisel, Interpretation of analysis by means of constructive functionals of finite types, Constructivity in Mathematics, Amsterdam (1959), 101-128.
[7] W. Craig, On axiomatizability with in a system, J. Symbolic Logic, 18 (1953), 30-32.
[8] J. B. Rosser, Gödel theorems for non constructive logics, J. Symbolic Logic, 2 (1937), 129-137.
[9] Hilbert Bernays, Grundlagen der Mathematik II.
[10] S. Feferman, Arithmetization of metamathematics in a general setting, Fund. Math., 49 (1960), 35-92.
[11] G. Gentzen, Beweisbarkeit und Unbeweisbarkeit von Anfangsfällen der transfiniten Induktion in der reinen Zahlentheorie, Math. Ann., 119 (1943), 140-161.
[12] K. Gödel, Zur intuitionistischen Arithmetik und Zahlentheorie, Ergebnisse eines math. Koll., 4 (1932), 34-38.
[13] T. Nishimura, On Gödel's theorem, J. Math. Soc. Japan, 13 (1961), 1-12.
[14] T. Nishimura, Consistency and impredicative statements, Ann. Japan Assoc. Philos. Sci. 2 (1963), 14-26.
[15] A. Mostowski, Some impredicative definitions in the axiomatic set-theory, Fund. Math., 37 (1950), 111-124.
[16] H. Wang, Truth definitions and consistency proofs, Trans. Amer. Math. Soc., 73 (1952), 243-275.
[17] G. Kreisel, On the interpretation of non finitist proofs part I, II, J. Symolic Logic, 16 (1951), 241-267 and 17 (1952), 43-58.

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