Transfinite type theory and provability of second order formulas

Tsuyoshi YUKAMI

doi:10.2969/jmsj/02940633

Tsuyoshi YUKAMI

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ジャーナルフリー

1977 年 29 巻 4 号 p. 633-654

DOI https://doi.org/10.2969/jmsj/02940633

詳細

Published: 1977 Received: 1975/09/25 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) P. B. Andrews, A transfinite type theory with type variables, North Holland, Amsterdam, 1965.
2) K. Gödel, Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I, Monatshefte für Mathematik und Physik, 38 (1931), 173-198.
3) S. Maehara, A system of simple type theory with type variables, Ann. Japan Assoc. Philos. Sci., 3 (1969), 131-137.
4) R. Montague, Set theory and higher order logic, in: Formal systems and recursive functions, ed. by J. Crossly and M. Dummett, North Holland, Amsterdam, 1964, 131-148.
5) K. Schütte, Syntactical and semantical properties of simple type theory, J. Symbolic Logic, 25 (1960), 305-326.
6) M. Takahashi, A proof of cut-elimination theorem in simple type theory, J. Math. Soc. Japan, 19 (1967), 399-410.
7) G. Takeuti, On a generalized logic calculus, Japan. J. Math., 23 (1953), 39-96.
8) T. Uesu, Two formal systems of simple type theory with type variables, Comment. Math. Univ. St. Paul., 19 (1970), 13-46.

Right : [1] P. B. Andrews, A transfinite type theory with type variables, North Holland, Amsterdam, 1965.
[2] K. Gödel, Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I, Monatshefte für Mathematik und Physik, 38 (1931), 173-198.
[3] S. Maehara, A system of simple type theory with type variables, Ann. Japan Assoc. Philos. Sci., 3 (1969), 131-137.
[4] R. Montague, Set theory and higher order logic, in: Formal systems and recursive functions, ed. by J. Crossly and M. Dummett, North Holland, Amsterdam, 1964, 131-148.
[5] K. Schütte, Syntactical and semantical properties of simple type theory, J. Symbolic Logic, 25 (1960), 305-326.
[6] M. Takahashi, A proof of cut-elimination theorem in simple type theory, J. Math. Soc. Japan, 19 (1967), 399-410.
[7] G. Takeuti, On a generalized logic calculus, Japan. J. Math., 23 (1953), 39-96.
[8] T. Uesu, Two formal systems of simple type theory with type variables, Comment. Math. Univ. St. Paul., 19 (1970), 13-46.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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