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Quasi-modal algebras. (English) Zbl 0999.06012

Summary: In this paper we introduce the class of Boolean algebras with an operator between the algebra and the set of ideals of the algebra. This is a generalization of the Boolean algebras with operators. We prove that there exists a duality between these algebras and the Boolean spaces with a certain relation. We also give some applications of this duality.

MSC:

06E25 Boolean algebras with additional operations (diagonalizable algebras, etc.)
03G05 Logical aspects of Boolean algebras
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