Some concepts of recursiveness on admissible ordinals

Masaru FUKUYAMA

doi:10.2969/jmsj/02330435

Masaru FUKUYAMA

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ジャーナルフリー

1971 年 23 巻 3 号 p. 435-451

DOI https://doi.org/10.2969/jmsj/02330435

詳細

Published: 1971 Received: 1970/05/19 Available on J-STAGE: 2006/09/29 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/09/29 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) J. Barwise, Infinitary logic and admissible sets, J. Symbolic Logic, 34 (1969), 226-252.
2) H. Hermes, Enumerability, decidability, computability, Springer-Verlag, 1965.
3) M. Hirano, Some definitions for recursive functions of ordinal numbers, Sci. Rep. Tokyo Kyoiku Daigaku sec. A., 10 (1969), 1-7.
4) S. Kripke, Transfinite recursions on admissible ordinals I and II, J. Symbolic Logic, 29 (1964), 161-162.
5) S. Kripke, Transfinite recursions, constructible sets and analogues of cardinals, mimeographed.
6) K. Kunen, Implicit definability and infinitary languages, J. Symbolic Logic, 33 (1968), 446-451.
7) R. Montague, Recursion theory as a branch of model theory, Logic, Methodology and Philosophy of Science III, North-Holland Pub. Co., 1968, 63-86.
8) M. Takahashi, Recursive functions of ordinal numbers and Lévy's hierarchy, Comment. Math. Univ. St. Paul., 17 (1969), 21-29.
9) G. Takeuti and A. Kino, On hierarchies of predicates of ordinal numbers, J. Math. Soc. Japan, 14 (1962), 199-232.
10) G. Takeuti, A formalization of the theory of ordinal numbers, J. Symbolic Logic, 30 (1965), 295-317.
11) H. Tanaka, On the HA-restricted ω-rule, mimeographed.
12) T. Tugué, On the partial recursive functions of ordinal numbers, J. Math. Soc. Japan, 16 (1964), 1-32.

Right : [1] J. Barwise, Infinitary logic and admissible sets, J. Symbolic Logic, 34 (1969), 226-252.
[2] H. Hermes, Enumerability, decidability, computability, Springer-Verlag, 1965.
[3] M. Hirano, Some definitions for recursive functions of ordinal numbers, Sci. Rep. Tokyo Kyoiku Daigaku sec. A., 10 (1969), 1-7.
[4] S. Kripke, Transfinite recursions on admissible ordinals I and II, J. Symbolic Logic, 29 (1964), 161-162.
[5] S. Kripke, Transfinite recursions, constructible sets and analogues of cardinals, mimeographed.
[6] K. Kunen, Implicit definability and infinitary languages, J. Symbolic Logic, 33 (1968), 446-451.
[7] R. Montague, Recursion theory as a branch of model theory, Logic, Methodology and Philosophy of Science III, North-Holland Pub. Co., 1968, 63-86.
[8] M. Takahashi, Recursive functions of ordinal numbers and Lévy's hierarchy, Comment. Math. Univ. St. Paul., 17 (1969), 21-29.
[9] G. Takeuti and A. Kino, On hierarchies of predicates of ordinal numbers, J. Math. Soc. Japan, 14 (1962), 199-232.
[10] G. Takeuti, A formalization of the theory of ordinal numbers, J. Symbolic Logic, 30 (1965), 295-317.
[11] H. Tanaka, On the HA-restricted ω-rule, mimeographed.
[12] T. Tugué, On the partial recursive functions of ordinal numbers, J. Math. Soc. Japan, 16 (1964), 1-32.

訂正日: 2006/09/29 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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