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Hilbert algebras with a necessity modal operator

Celani S.A., Montangie D.

Reports on Mathematical Logic

2014

Vol. 49

47--77

We introduce the variety of Hilbert algebras with a modal operator , called H-algebras. The variety of H-algebras is the algebraic counterpart of the {→;]}fragment of the intuitionitic modal logic IntK. We will study the theory of representation and we will give a topological duality for the variety of H-algebras. We are going to use these results to prove that the basic implicative modal logic IntK→ and some axiomatic extensions are canonical. We shall also to determine the simple and subdirectly irreducible algebras in some subvarieties of H-algebras.