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

Moto-o TAKAHASHI

doi:10.2969/jmsj/01940399

Moto-o TAKAHASHI

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JOURNAL FREE ACCESS

1967 Volume 19 Issue 4 Pages 399-410

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

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Published: 1967 Received: January 16, 1967 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) 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.

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

Date of correction: September 26, 2006 Reason for correction: - Correction: CITATION Details: 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.

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

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