A general method of axiomatizing fragments

Tadahiro UESU

doi:10.2969/jmsj/04320413

Tadahiro UESU

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JOURNAL FREE ACCESS

1991 Volume 43 Issue 2 Pages 413-432

DOI https://doi.org/10.2969/jmsj/04320413

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Published: 1991 Received: July 16, 1990 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) J. Akaboshi, On elimination theorems (in Japanese), Master thesis, Kyushu University, 1981.
2) G. Gentzen, Unter Suchungen über das Logische Schliessen, Mathematische Zeitschrift, 39 (1981), 176-210, 405-431.
3) N. Motohashi, An axiomatization theorem, J. Math. Soc. Japan, 34 (1982), 551-560.
4) N. Motohashi, Approximation theory of uniqueness conditions by existence conditions, Fund. Math., 120 (1984), 127-142.
5) J. R. Shoenfield, Mathematical Logic, Addison-Wesley, Reading, 1967.
6) C. Smorynski, On axiomatizing fragments, J. Symbolic Logic, 42 (1977), 530-544.
7) C. Smorynski, The axiomatization problem for fragments, Ann. Math. Logic, 14 (1978), 193-221.
8) G. Takeuti, Proof Theory, 2nd ed., Studies in Logic and the Foundation of Mathematics, 81, North-Holland, Amsterdam, 1987.
9) T. Uesu, An Axiomatization of the apartness fragment of the theory DLO⁺ of dense linear order, Lecture Notes in Math., 1104 Springer-Verlag, 1984, pp. 453-475.
10) D, van Dalen and R. Statman, Equality in the presence of apartness, (eds. J. Hintikka, et al) Essays on mathematical and philosophical logic, D. Reidel, Dordrecht, 1978, pp. 95-116.

Right : [1] J. Akaboshi, On elimination theorems (in Japanese), Master thesis, Kyushu University, 1981.
[2] G. Gentzen, Unter Suchungen über das Logische Schliessen, Mathematische Zeitschrift, 39 (1981), 176-210, 405-431.
[3] N. Motohashi, An axiomatization theorem, J. Math. Soc. Japan, 34 (1982), 551-560.
[4] N. Motohashi, Approximation theory of uniqueness conditions by existence conditions, Fund. Math., 120 (1984), 127-142.
[5] J. R. Shoenfield, Mathematical Logic, Addison-Wesley, Reading, 1967.
[6] C. Smorynski, On axiomatizing fragments, J. Symbolic Logic, 42 (1977), 530-544.
[7] C. Smorynski, The axiomatization problem for fragments, Ann. Math. Logic, 14 (1978), 193-221.
[8] G. Takeuti, Proof Theory, 2nd ed., Studies in Logic and the Foundation of Mathematics, 81, North-Holland, Amsterdam, 1987.
[9] T. Uesu, An Axiomatization of the apartness fragment of the theory DLO⁺ of dense linear order, Lecture Notes in Math., 1104 Springer-Verlag, 1984, pp. 453-475.
[10] D. van Dalen and R. Statman, Equality in the presence of apartness, (eds. J. Hintikka, et al) Essays on mathematical and philosophical logic, D. Reidel, Dordrecht, 1978, pp. 95-116.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

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