References
W. E. Beth, “On Padoa's method in the theory of definitions,” Indag. Math.,15, No. 4, 330–339 (1953).
J. Barwise and S. Feferman (eds), Model-Theoretic Logics, Springer-Verlag, New York (1985).
L. L. Maksimova, “Definability theorems in normal extensions of the provability logic,” Studia Logica,48, No. 4, 495–507 (1989).
L. Henkin, J. D. Monk, and A. Tarski, Cylindric Algebras, Part 2, North-Holland, Amsterdam (1985).
L. L. Maksimova, Interpolation, the Beth Property and Temporal Logic “of Tomorrow” [Preprint], Akad. Nauk SSSR Sibirsk. Otdel., Inst. Mat., Novosibirsk, 1989.
L. L. Maksimova, “Interpolation theorems in modal logics and amalgamated varieties of topoboolean algebras,” Algebra i Logika,18, No. 5, 556–586 (1979).
W. J. Blok, “Pretabular varieties of modal algebras,” Studia Logica,39, No. 2/3, 101–124 (1980).
W. J. Blok and D. Pigozzi, “Algebraizable logics,” Mem. Amer. Math. Soc.,77, No. 396 (1989).
G. Kreisel, “Explicit definability in intuitionistic logic,” J. Symbolic Logic,25, 389–390 (1960).
K. Segerberg, An Essay in Classical Modal Logic, Uppsala (1971).
H. Rasiowa and R. Sikorski, The Mathematics of Metamathematics [Russian translation] Nauka, Moscow (1972).
A. I. Mal'tsev, Algebraic Systems [in Russian], Nauka, Moscow (1970).
D. Gabbay, “Craig's interpolation theorem for modal logic,” in: Proc. Conference on Math. Logic. London'70, Springer, Berlin, 1972, pp. 111–127.
W. Rautenberg, “Modal tableau calculi and interpolation,” J. Philos. Logic,12, 403–423 (1983).
L. L. Maksimova, “On interpolation in normal modal logics,” in: Nonclassical Logics [in Russian], Stiintsa, Kishinëv, 1987, pp. 40–56.
Additional information
Novosibirsk. Translated fromSibirskiî Matematicheskiî zhurnal, Vol. 33, No. 6, pp. 118–130, November–December, 1992.
Translated by the author
Rights and permissions
About this article
Cite this article
Maksimova, L.L. An analog of Beth's theorem in normal extensions of the modal logic K4. Sib Math J 33, 1052–1065 (1992). https://doi.org/10.1007/BF00971028
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00971028