On hierarchies of predicates of ordinal numbers

Gaisi TAKEUTI; Akiko KINO

doi:10.2969/jmsj/01420199

Gaisi TAKEUTI, Akiko KINO

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JOURNAL FREE ACCESS

1962 Volume 14 Issue 2 Pages 199-232

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

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Published: 1962 Received: September 04, 1961 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: CITATION Details: 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.

Date of correction: September 26, 2006 Reason for correction: - Correction: PDF FILE Details: -

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