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Varieties of monadic Heyting algebras. I. (English) Zbl 0964.06008
Summary: This paper deals with varieties of monadic Heyting algebras, which are algebraic models of intuitionistic modal logic MIPC. We investigate semisimple, locally finite, finitely approximated and splitting varieties of monadic Heyting algebras as well as varieties with the disjunction and the existence properties. The investigation of monadic Heyting algebras clarifies the correspondence between intuitionistic modal logics over MIPC and superintuitionistic predicate logics and provides us with solutions of several problems raised by H. Ono [Rep. Math. Log. 21, 55-67 (1987; Zbl 0676.03016)].

MSC:
06D20 Heyting algebras (lattice-theoretic aspects)
03B45 Modal logic (including the logic of norms)
03G25 Other algebras related to logic
03B55 Intermediate logics
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