Varieties of monadic Heyting algebras. Part I

Studia Logica 61 (3):367-402 (1998)
Abstract
This paper deals with the varieties of monadic Heyting algebras, 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 the solutions of several problems raised by Ono [35].
Keywords intuitionistic modal logic  monadic Heyting algebras  relatively complete sub-algebras  monadic filters  monadic ideals  splittings
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