Characterization of subdirectly irreducible heyting algebras with negative tense operators

Abstract

Ma and Li established Intuitionistic Propositional Logic with Galois negations (IGN). These logics can be viewed as the ordered dualization of Ewald’s intuitionistic tense logic IKt, where Galois negations function as the ordered duals of residuated pairs of tense operators. We introduced the concept of negative tense operators on Heyting algebras and defined the variety of tense H-algebras. This new variety of algebras serves as the algebraic semantics for IGN. In this paper, we extend our investigation into tense H-algebras, focusing specifically on their topological properties. Particularly, we provide a topological characterization of subdirectly irreducible tense H-algebras.