On hierarchies of predicates of ordinal numbers

Gaisi TAKEUTI; Akiko KINO

doi:10.2969/jmsj/01420199

Gaisi TAKEUTI, Akiko KINO

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ジャーナルフリー

1962 年 14 巻 2 号 p. 199-232

DOI https://doi.org/10.2969/jmsj/01420199

詳細

Published: 1962 Received: 1961/09/04 Available on J-STAGE: 2006/09/26 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/09/26 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) J. W. Addison, Some consequences of the axiom of constructibility, Fund. Math., 46 (1959), 337-357.
2) J. W. Addison, Separation principles in the hierarchies of classical and effective descriptive set theory, Fund. Math., 46 (1958), 123-134.
3) A. Church and S. C. Kleene, Formal definitions in the theory of ordinal numbers, Fund. Math., 28 (1936), 11-21.
4) K. Gödel, The consistency of the axiom of choice and of the generalized continuum hypothesis with the axioms of set theory, Princeton, 1940.
5) S. C. Kleene, On the forms of the predicates in the theory of constructive ordinals, Amer. J. Math., 66 (1944), 41-58.
6) S. C. Kleene, Introduction to metamathematics, New York, Amsterdam and Groningen, 1952.
7) S. C. Kleene, Arithmetical predicates and function quantifiers, Trans. Amer. Math. Soc., 79 (1955), 312-340.
8) S. C. Kleene, Hierarchies of number-theoretic predicates, Bull. Amer. Math. Soc., 61 (1955), 193-213.
9) S.C. Kleene, On the forms of the predicates in the theory of constructive ordinals (second paper), Amer. J. Math., 77 (1955), 405-428.
10) M. Kondo, Sur l'uniformisation des complementaires analytiques et les ensembles projectifs de la second classe, Jap. J. Math., 15 (1938), 197-230.
11) M. Kondo, Sur l'uniformisation des ensembles nommables, C.R. Acad. Sci. Paris 246 (1959), 2712-2715.
12) D.L. Kreider and H. Rogers. Jr., Constructive versions of ordinal number classes, Trans. Amer. Math. Soc., 100 (1961), 325-369.
13) C. Kuratowski, Sur la geometrisation des types d'ordre dénombrable, Fund. Math., 28 (1937), 167-185.
14) C. Spector, Recursive well-orderings, J. Symbolic Logic, 20 (1955), 151-163.
15) G. Takeuti, Construction of the set theory from the theory of ordinal numbers, J. Math. Soc. Japan, 6 (1954), 196-220.
16) G. Takeuti, On the theory of ordinal numbers, J. Math. Soc. Japan, 9 (1957), 93-113.
17) G. Takeuti, On the recursive functions of ordinal numbers, J. Math. Soc. Japan, 12 (1960), 119-128.
18) J. R. Shoenfield, The problem of predicativity, Essays on the foundations of mathematics, 132-142, Amsterdam, 1962.
19) H. Putnam, Uniquness ordinal in higher constructive number classes, Essays on the foundations of mathematics., 190-206.

Right : [1] J. W. Addison, Some consequences of the axiom of constructibility, Fund. Math., 46 (1959), 337-357.
[2] J. W. Addison, Separation principles in the hierarchies of classical and effective descriptive set theory, Fund. Math., 46 (1958), 123-134.
[3] A. Church and S. C. Kleene, Formal definitions in the theory of ordinal numbers, Fund. Math., 28 (1936), 11-21.
[4] K. Gödel, The consistency of the axiom of choice and of the generalized continuum hypothesis with the axioms of set theory, Princeton, 1940.
[5] S. C. Kleene, On the forms of the predicates in the theory of constructive ordinals, Amer. J. Math., 66 (1944), 41-58.
[6] S. C. Kleene, Introduction to metamathematics, New York, Amsterdam and Groningen, 1952.
[7] S. C. Kleene, Arithmetical predicates and function quantifiers, Trans. Amer. Math. Soc., 79 (1955), 312-340.
[8] S. C. Kleene, Hierarchies of number-theoretic predicates, Bull. Amer. Math. Soc., 61 (1955), 193-213.
[9] S. C. Kleene, On the forms of the predicates in the theory of constructive ordinals (second paper), Amer. J. Math., 77 (1955), 405-428.
[10] M. Kondô, Sur l'uniformisation des complementaires analytiques et les ensembles projectifs de la second classe, Jap. J. Math., 15 (1938), 197-230.
[11] M. Kondô, Sur l'uniformisation des ensembles nommables, C. R. Acad. Sci. Paris 246 (1959), 2712-2715.
[12] D. L. Kreider and H. Rogers. Jr., Constructive versions of ordinal number classes, Trans. Amer. Math. Soc., 100 (1961), 325-369.
[13] C. Kuratowski, Sur la geometrisation des types d'ordre dénombrable, Fund. Math., 28 (1937), 167-185.
[14] C. Spector, Recursive well-orderings, J. Symbolic Logic, 20 (1955), 151-163.
[15] G. Takeuti, Construction of the set theory from the theory of ordinal numbers, J. Math. Soc. Japan, 6 (1954), 196-220.
[16] G. Takeuti, On the theory of ordinal numbers, J. Math. Soc. Japan, 9 (1957), 93-113.
[17] G. Takeuti, On the recursive functions of ordinal numbers, J. Math. Soc. Japan, 12 (1960), 119-128.
[18] J. R. Shoenfield, The problem of predicativity, Essays on the foundations of mathematics, 132-142, Amsterdam, 1962.
[19] H. Putnam, Uniquness ordinal in higher constructive number classes, Essays on the foundations of mathematics, 190-206.

訂正日: 2006/09/26 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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