Monadicity in topological pseudo-boolean algebras

Abstract

We study four subclasses of topological pseudo-Boolean algebras representing increasingly strong intuítionistic counterparts of monadic Boolean algebras. The fourteen equivalent classical conditions are shown to split into six non-equivalent sets of equivalent conditions, whose inter-connections are all determined. We also deal with several algebraic-logic properties of our classes, such as regular, dense, Peircean elements, and others. We conclude that a closure operator derived from an interior one is not meaningless in this context of intuítionistic modal logic.