A note on predicates of ordinal numbers

Akiko KINO; Gaisi TAKEUTI

doi:10.2969/jmsj/01440367

Akiko KINO, Gaisi TAKEUTI

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JOURNAL FREE ACCESS

1962 Volume 14 Issue 4 Pages 367-378

DOI https://doi.org/10.2969/jmsj/01440367

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Published: 1962 Received: March 22, 1962 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 set theory, Fund. Math., 46 (1959), 123-134.
3) K. Gödel, The consistency of the axiom of choice and of generalized continuum hypothesis with the axioms of set theory, Princeton, 1940.
4) S. C. Kleene, Recursive functionals and quantifiers of finite types I, Trans. Amer. Math. Soc., 91 (1959), 1-52.
5) G. Takeuti, Construction of the set theory from the theory of ordinal numbers, J. Math. Soc. Japan, 6 (1954), 196-220.
6) G. Takeuti, On the theory of ordinal numbers, J. Math. Soc. Japan, 9 (1957), 93-113.
7) G. Takeuti, On the recursive functions of ordinal numbers, J. Math. Soc. Japan, 12 (1960), 119-128.
8) G. Takeuti and A. Kino, On hierarchies of predicates of ordinal numbers, J. Math. Soc. Japan, 14 (1962), 199-232.
9) T. Tugué, Predicates recursive in a type-2 object and Kleene hierarchies, Comment. Math. Univ. St. Paul., 8 (1959), 97-117.

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 set theory, Fund. Math., 46 (1959), 123-134.
[3] K. Gödel, The consistency of the axiom of choice and of generalized continuum hypothesis with the axioms of set theory, Princeton, 1940.
[4] S. C. Kleene, Recursive functionals and quantifiers of finite types I, Trans. Amer. Math. Soc., 91 (1959), 1-52.
[5] G. Takeuti, Construction of the set theory from the theory of ordinal numbers, J. Math. Soc. Japan, 6 (1954), 196-220.
[6] G. Takeuti, On the theory of ordinal numbers, J. Math. Soc. Japan, 9 (1957), 93-113.
[7] G. Takeuti, On the recursive functions of ordinal numbers, J. Math. Soc. Japan, 12 (1960), 119-128.
[8] G. Takeuti and A. Kino, On hierarchies of predicates of ordinal numbers, J. Math. Soc. Japan, 14 (1962), 199-232.
[9] T. Tugué, Predicates recursive in a type-2 object and Kleene hierarchies, Comment. Math. Univ. St. Paul., 8 (1959), 97-117.

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

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