A variation of Lyndon-Keisler's homomorphism theorem and its applications to interpolation theorems

Tsuyoshi FUJIWARA

doi:10.2969/jmsj/03020287

Tsuyoshi FUJIWARA

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JOURNAL FREE ACCESS

1978 Volume 30 Issue 2 Pages 287-302

DOI https://doi.org/10.2969/jmsj/03020287

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Published: 1978 Received: August 30, 1976 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) C. C. Chang and H. J. Keisler, Model Theory, North-Holland, Amsterdam, 1973.
2) W. Craig, Linear reasoning. A new form of the Herbrand-Gentzen theorem, J. Symbolic Logic, 22 (1957), 250-268.
3) L. Henkin, An extension of the Craig-Lyndon interpolation theorem, J. Symbolic Logic, 28 (1963), 201-216.
4) H. J. Keisler, Theory of models with generalized atomic formulas, J. Symbolic Logic, 25 (1960), 1-26.
5) H. J. Keisler, Model Theory for Infinitary Logic, North-Holland, Amsterdam, 1971.
6) S. C. Kleene, Introduction to Metamathematics, D. Van Nostrand, Princeton, 1952.
7) E. G. K. Lopez-Escobar, An interpolation theorem for denumerably long formulas, Fund. Math., LVII (1965), 253-272.
8) R. C. Lyndon, An interpolation theorem in the predicate calculus, Pacific J. Math., 9 (1959), 129-42.
9) R. C. Lyndon, Properties preserved under homomorphism, Pacific J. Math., 9 (1959), 143-154.
10) N. Motohashi, Interpolation theorem and characterization theorem, Ann. Japan Assoc. Philos. Sci., 4 (1972), 85-150.
11) A. Oberschelp, On the Craig-Lyndon interpolation theorem, Notices of Amer. Math. Soc., 14 (1967), 142.
12) A. Oberschelp, On the Craig-Lyndon interpolation theorem, J. Symbolic Logic, 33 (1968), 271-274.
13) A. Robinson, A result on consistency and its application to the theory of definition, Koninkl. Ned. Akad. Wetensch. Proc. Ser. A, 59 (=Indag. Math., 18) (1956), 47-58.
14) A. Robinson, Introduction to Model Theory and to the Metamathematics of Algebra, 2nd, revised printing, North-Holland, Amsterdam, 1974.
15) J. R. Shoenfield, Mathematical Logic, Addison-Wesley, Reading, Massachusetts, 1967.

Right : [1] C. C. Chang and H. J. Keisler, Model Theory, North-Holland, Amsterdam, 1973.
[2] W. Craig, Linear reasoning. A new form of the Herbrand-Gentzen theorem, J. Symbolic Logic, 22 (1957), 250-268.
[3] L. Henkin, An extension of the Craig-Lyndon interpolation theorem, J. Symbolic Logic, 28 (1963), 201-216.
[4] H. J. Keisler, Theory of models with generalized atomic formulas, J. Symbolic Logic, 25 (1960), 1-26.
[5] H. J. Keisler, Model Theory for Infinitary Logic, North-Holland, Amsterdam, 1971.
[6] S. C. Kleene, Introduction to Metamathematics, D. Van Nostrand, Princeton, 1952.
[7] E. G. K. Lopez-Escobar, An interpolation theorem for denumerably long formulas, Fund. Math., LVII (1965), 253-272.
[8] R. C. Lyndon, An interpolation theorem in the predicate calculus, Pacific J. Math., 9 (1959), 129-42.
[9] R. C. Lyndon, Properties preserved under homomorphism, Pacific J. Math., 9 (1959), 143-154.
[10] N. Motohashi, Interpolation theorem and characterization theorem, Ann. Japan Assoc. Philos. Sci., 4 (1972), 85-150.
[11] A. Oberschelp, On the Craig-Lyndon interpolation theorem, Notices of Amer. Math. Soc., 14 (1967), 142.
[12] A. Oberschelp, On the Craig-Lyndon interpolation theorem, J. Symbolic Logic, 33 (1968), 271-274.
[13] A. Robinson, A result on consistency and its application to the theory of definition, Koninkl. Ned. Akad. Wetensch. Proc. Ser. A, 59 (=Indag. Math., 18) (1956), 47-58.
[14] A. Robinson, Introduction to Model Theory and to the Metamathematics of Algebra, 2nd, revised printing, North-Holland, Amsterdam, 1974.
[15] J. R. Shoenfield, Mathematical Logic, Addison-Wesley, Reading, Massachusetts, 1967.

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