On two systems for arithmetic Dedicated to Professor Y. Akizuki on his sixtieth birthday

Toshio NISHIMURA; Hisao TANAKA

doi:10.2969/jmsj/01730244

On two systems for arithmetic

Dedicated to Professor Y. Akizuki on his sixtieth birthday

Toshio NISHIMURA, Hisao TANAKA

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1965 Volume 17 Issue 3 Pages 244-280

DOI https://doi.org/10.2969/jmsj/01730244

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Published: 1965 Received: August 31, 1963 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) A. Grzegorczyk, A. Mostowski and C. Ryll-Nardzewski, The classical and the ω-complete arithmetic, J. Symbolic Logic, 23 (1958), 188-206.
2) S. C. Kleene, Introduction to Metamathematics, Amsterdam, Groningen, New York and Toronto, 1952, pp. 550.
3) S. C. Kleene, On the forms of predicates on the theory of constructive ordinals, I, II, Amer. J. Math., 66 (1944), 41-58 and Vol. 77 (1955), 405-428.
4) S. C. Kleene, Arithmetical predicates and function quantifiers, Trans. Amer. Math. Soc., 79 (1955), 312-340.
5) S. Maehara and G. Takeuti, A formal system of first-order predicate calculus with infinitely long expressions, J. Math. Soc. Japan, 13 (1961), 356-370.
6) A. Mostowski, A generalization of the incompleteness theorem, Fund. Math., 49 (1961), 205-232.
7) G. Takeuti and A. Kino, On predicates with constructive infinitely long expressions, J. Math. Soc. Japan, 15 (1963), 176-190.

Right : [1] A. Grzegorczyk, A. Mostowski and C. Ryll-Nardzewski, The classical and the ω-complete arithmetic, J. Symbolic Logic, 23 (1958), 188-206.
[2] S. C. Kleene, Introduction to Metamathematics, Amsterdam, Groningen, New York and Toronto, 1952, pp. 550.
[3] S. C. Kleene, On the forms of predicates on the theory of constructive ordinals, I, II, Amer. J. Math., 66 (1944), 41-58 and Vol. 77 (1955), 405-428.
[4] S. C. Kleene, Arithmetical predicates and function quantifiers, Trans. Amer. Math. Soc., 79 (1955), 312-340.
[5] S. Maehara and G. Takeuti, A formal system of first-order predicate calculus with infinitely long expressions, J. Math. Soc. Japan, 13 (1961), 356-370.
[6] A. Mostowski, A generalization of the incompleteness theorem, Fund. Math., 49 (1961), 205-232.
[7] G. Takeuti and A. Kino, On predicates with constructive infinitely long expressions, J. Math. Soc. Japan, 15 (1963), 176-190.

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

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