Abstract
Algebraic counterparts are found for the Beth, projective Beth, interpolation, disjunction, and existential properties of superintuitionistic first-order logics.
REFERENCES
D. E. Tishkovskii, “Algebraic semantics for superintuitionistic predicate logics,” Algebra Logika, 38, No. 1, 68-95 (1999).
Yu. L. Ershov and E. A. Palyutin, Mathematical Logic [in Russian], Nauka, Moscow (1979).
H. Rasiowa and R. Sikorski, The Mathematics of Metamathematics, Monografien Matematyczne, Warsaw (1963).
L. Maksimova, “On maximal intermediate logics with disjunction property,” Stud. Log., 45, No. 1, 69-75 (1986).
A. G. Dragalin, Mathematical Intuitionism. Introduction to Proof Theory [in Russian], Nauka, Moscow (1979).
L. Maksimova, “Explicit and implicit definability in modal and related logics,” Bull. Sect. Log., Univ. Łodź, Dep. Log., 27, Nos. 1/2, 36-39 (1998).
L. L. Maksimova, “Craig's theorem in superintuitionistic logics and amalgamable varieties of pseudo-Boolean algebras,” Algebra Logika, 16, No. 6, 643-681 (1977).
L. L. Maksimova, “Interpolation theorems in modal logics and amalgamable varieties of topoboolean algebras,” Algebra Logika, 18, No. 5, 556-586 (1979).
L. L. Maksimova, “Modal logics and varieties of modal algebras: Beth properties, interpolation, and amalgamation,” Algebra Logika, 31, No. 2, 145-166 (1992).
J. Czelakowski, “Logical matrices and the amalgamation property,” Stud. Log., 41, No. 4, 329-341 (1982).
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Tishkovskii, D.E. Algebraic Counterparts for Some Properties of Superintuitionistic Predicate Logics. Algebra and Logic 40, 122–134 (2001). https://doi.org/10.1023/A:1010217022641
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DOI: https://doi.org/10.1023/A:1010217022641