References
W. Craig, “Three uses of the Herbrand-Gentzen theorem in relating model theory and proof theory,” J. Symbolic Logic,22, 269–285 (1957).
K. Schütte, “Der Interpolationssatz der intuitionistischen Prädikatenlogik,” Math. Ann.,148, 192–200 (1962).
D. Gabbay, “Semantic proof of the Craig interpolation theorem for intuitionistic logic and extensions it,” in: Logic Colloquium'69, Amsterdam, 1970, pp. 391–410.
L. L. Maksimova, “Craig's theorem in superintuitionistic logics and amalgamable varieties”, Algebra i Logika,16, No. 6, 643–681 (1977).
L. L. Maksimova, “Interpolation in predicate logics with equality,” in: Abstracts: The 10th International Congress of Logic, Methodology and Philosophy of Science, Florence, Italy, 1995, p. 154.
H. Ono, “Some problems in intermediate predicate logics,” Rep. Math. Logic,21, 55–67 (1987).
A. Church, Introduction to Mathematical Logic. Vol. 1, Princeton Univ. Press, Princeton (New Jersey) (1956).
S. C. Kleene, Introduction to Metamathematics, D. Van Nostrad Company, Inc., New York and Toronto (1952).
S. C. Kleene, Mathematical Logic, John Wiley & Sons, Inc., New York, London, and Sidney (1967).
Y. Komori, “Logics without Craig's interpolation property,” Proc. Japan Acad. Ser. A. Math. Sci.,54(A), No. 2, 46–48 (1978).
Yu. L. Ershov and E. A. Palyutin, Mathematical Logic [in Russian], Nauka, Moscow (1979).
Additional information
The research was supported by the Russian Foundation for Humanities (Grant 97-03-04089).
Novosibirsk. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 39, No. 1, pp. 172–180, January–February. 1998.
Rights and permissions
About this article
Cite this article
Tishkovsky, D.E. Interpolation property and superintuitionistic predicate logics. Sib Math J 39, 151–158 (1998). https://doi.org/10.1007/BF02732369
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02732369