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Algebraic counterparts for some properties of superintuitionistic predicate logics. (Russian, English) Zbl 0983.03019
Algebra Logika 40, No. 2, 218-242 (2001); translation in Algebra Logic 40, No. 2, 122-134 (2001).
In Algebra Logic 38, No. 1, 36-50 (1999; Zbl 0924.03112), the author introduced and treated the class of quasicylindric algebras. It was proven that every superintuitionistic predicate logic is complete with respect to some variety of quasicylindric algebras. In the article under review, algebraic counterparts are found for the Beth, projective Beth, interpolation, disjunction, and existential properties of superintuitionistic first-order logics (in terms of the corresponding varieties of quasicylindric algebras).
03B55 Intermediate logics
03G25 Other algebras related to logic
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