A proof of cut-elimination theorem in simple type-theory

Moto-o TAKAHASHI

doi:10.2969/jmsj/01940399

Moto-o TAKAHASHI

著者情報

ジャーナルフリー

1967 年 19 巻 4 号 p. 399-410

DOI https://doi.org/10.2969/jmsj/01940399

詳細

Published: 1967 Received: 1967/01/16 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) G. Gentzen, Untersuchungen über das logische Schliessen I, Math. Z., 39 (1934), 176-210.
2) K. Schütte, Syntactical and semantical properties of simple type theory, J. Symb. Logic, 25 (1960), 305-326.
3) W. Tait, A non-constructive proof of Gentzen's Hauptsatz for second order predicate logic, Bull. Amer. Math. Soc., 72 (1966), 980-983.
4) G. Takeuti, On a generalized logic calculus, Japan. J. Math., 23 (1953), 39-96.
5) A. Tarski, The concept of truth in formalized languages, logic, semantics, metamathematics, Oxford Univ. Press, 1956, 152-278.
6) S. Titani, An algebraic formulation of cut-elimimation theorem, J. Math. Soc. Japan, 17 (1965), 72-83.
7) T. Uesu, On Zermelo's set-theory and the simple type-theory with the axiom of infinity, Comment. Math. Univ. St. Paul., 15 (1966), 49-59.
8) L. Henkin, Completeness in the theory of types, J. Symb. Logic, 15 (1950), 81-91.

Right : [1] G. Gentzen, Untersuchungen über das logische Schliessen I, Math. Z., 39 (1934), 176-210.
[2] K. Schütte, Syntactical and semantical properties of simple type theory, J. Symb. Logic, 25 (1960), 305-326.
[3] W. Tait, A non-constructive proof of Gentzen's Hauptsatz for second order predicate logic, Bull. Amer. Math. Soc., 72 (1966), 980-983.
[4] G. Takeuti, On a generalized logic calculus, Japan. J. Math., 23 (1953), 39-96.
[5] A. Tarski, The concept of truth in formalized languages, logic, semantics, metamathematics, Oxford Univ. Press, 1956, 152-278.
[6] S. Titani, An algebraic formulation of cut-elimimation theorem, J. Math. Soc. Japan, 17 (1965), 72-83.
[7] T. Uesu, On Zermelo's set-theory and the simple type-theory with the axiom of infinity, Comment. Math. Univ. St. Paul., 15 (1966), 49-59.
[8] L. Henkin, Completeness in the theory of types, J. Symb. Logic, 15 (1950), 81-91.

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

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] G. Gentzen, Untersuchungen über das logische Schliessen I, Math. Z., 39 (1934), 176-210.
[2] K. Schütte, Syntactical and semantical properties of simple type theory, J. Symb. Logic, 25 (1960), 305-326.
[3] W. Tait, A non-constructive proof of Gentzen's Hauptsatz for second order predicate logic, Bull. Amer. Math. Soc., 72 (1966), 980-983.
[4] G. Takeuti, On a generalized logic calculus, Japan. J. Math., 23 (1953), 39-96.
[5] A. Tarski, The concept of truth in formalized languages, logic, semantics, metamathematics, Oxford Univ. Press, 1956, 152-278.
[6] S. Titani, An algebraic formulation of cut-elimimation theorem, J. Math. Soc. Japan, 17 (1965), 72-83.
[7] T. Uesu, On Zermelo's set-theory and the simple type-theory with the axiom of infinity, Comment. Math. Univ. St. Paul., 15 (1966), 49-59.
[8] L. Henkin, Completeness in the theory of types, J. Symb. Logic, 15 (1950), 81-91.

Right : 1) G. Gentzen, Untersuchungen über das logische Schliessen I, Math. Z., 39 (1934), 176-210.
2) K. Schütte, Syntactical and semantical properties of simple type theory, J. Symb. Logic, 25 (1960), 305-326.
3) W. Tait, A non-constructive proof of Gentzen's Hauptsatz for second order predicate logic, Bull. Amer. Math. Soc., 72 (1966), 980-983.
4) G. Takeuti, On a generalized logic calculus, Japan. J. Math., 23 (1953), 39-96.
5) A. Tarski, The concept of truth in formalized languages, logic, semantics, metamathematics, Oxford Univ. Press, 1956, 152-278.
6) S. Titani, An algebraic formulation of cut-elimimation theorem, J. Math. Soc. Japan, 17 (1965), 72-83.
7) T. Uesu, On Zermelo's set-theory and the simple type-theory with the axiom of infinity, Comment. Math. Univ. St. Paul., 15 (1966), 49-59.
8) L. Henkin, Completeness in the theory of types, J. Symb. Logic, 15 (1950), 81-91.

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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