On Heyting algebras with negative tense operators II

Ma and Li (2023, Stud. Log., 111, 21–56) established Intuitionistaic Propositional Logic with Galois negations (IGN). These logics may be regarded as the ordered duals of Ewald’s intuitionistic tense logic IKt, with Galois negations acting as the ordered duals of residuated pairs of tense operators. In Almiñana et al. (2023, Stud. Log., 111, 1015–1036), we introduced the notion of negative tense operators on Heyting algebras and defined the variety of tense H-algebras. This new variety provides the algebraic semantics for IGN. In this paper, we extend our investigation of tense H-algebras, with a particular focus on their topological properties. In particular, we provide a topological characterization of subdirectly irreducible tense H-algebras.