A formal system of first-order predicate calculus with infinitely long expressions

Shôji MAEHARA; Gaisi TAKEUTI

doi:10.2969/jmsj/01340357

Shôji MAEHARA, Gaisi TAKEUTI

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1961 Volume 13 Issue 4 Pages 357-370

DOI https://doi.org/10.2969/jmsj/01340357

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Published: 1961 Received: April 03, 1961 Available on J-STAGE: August 29, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: August 29, 2006 Reason for correction: - Correction: AUTHOR Details: Wrong : Shoji MAEHARA¹⁾, Gaisi TAKEUTI²⁾
Right : Shôji MAEHARA¹⁾, Gaisi TAKEUTI²⁾

Date of correction: August 29, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) W. Craig, Linear reasoning. A new form of the Herbrand-Gentzen theorem, J. Symbolic Logic, 22 (1957), 250-268.
2) G. Gentzen, Untersuchungen über das logische Schliellen, Math. Z., 39 (1935), 176-210, 405-431.
3) K. Gödel, Die Vollstandigkeit der Axiome des logischen Funktionenkalkuls, Monatsh. f. Math. Phys., 37 (1930), 349-360.
4) D. Hilbert and P. Bernays, Gundlangen der Mathematik, Bd. 2, Berlin, 1939.
5) C. Karp, Independence proofs in predicate logic with infinitely long expressions. Lecture in International Congress for Logic, Methodology and Philosophy of Science 1960, Stanford.
6) S.C. Kleene, Introduction to metamathematics, Amsterdam-Groningen, 1952.
7) S. Maehara, The predicate calculus with ε-symbol, J. Math. Soc. Japan, 7 (1955), 323-344.
8) K. Schütte, Ein System des verknüpfen den SchlieBens, Archiv f . math. Logik u. Grundlagenforschung 2 (1956), 55-67.
9) D. Scott and A. Tarski, The sentential calculus with infinitely long expressions, Colloq. Math., 6 (1958), 165-170.

Right : [1] W. Craig, Linear reasoning. A new form of the Herbrand-Gentzen theorem, J. Symbolic Logic, 22 (1957), 250-268.
[2] G. Gentzen, Untersuchungen über das logische Schließen, Math. Z., 39 (1935), 176-210, 405-431.
[3] K. Gödel, Die Vollständigkeit der Axiome des logischen Funktionenkalküls, Monatsh. f. Math. Phys., 37 (1930), 349-360.
[4] D. Hilbert and P. Bernays, Gundlangen der Mathematik, Bd. 2, Berlin, 1939.
[5] C. Karp, Independence proofs in predicate logic with infinitely long expressions. Lecture in International Congress for Logic, Methodology and Philosophy of Science 1960, Stanford.
[6] S. C. Kleene, Introduction to metamathematics, Amsterdam-Groningen, 1952.
[7] S. Maehara, The predicate calculus with ε-symbol, J. Math. Soc. Japan, 7 (1955), 323-344.
[8] K. Schütte, Ein System des verknüpfen den Schließens, Archiv f. math. Logik u. Grundlagenforschung 2 (1956), 55-67.
[9] D. Scott and A. Tarski, The sentential calculus with infinitely long expressions, Colloq. Math., 6 (1958), 165-170.

Date of correction: August 29, 2006 Reason for correction: - Correction: PDF FILE Details: -

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