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<p>In (Intuitionistic propositional logic with galois negations. Stud Logica 111:21–56, 2023) , 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. In Almiñana et al. (On heyting algebras with negative tense operators. Stud Logica 111:1015–1036, 2023), 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.</p>

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Characterization of subdirectly irreducible heyting algebras with negative tense operators

  • 期刊论文

  • 发表日期：

    2026年1月16日

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  • Federico Almiñana,
  • Gustavo Pelaitay

摘要

In (Intuitionistic propositional logic with galois negations. Stud Logica 111:21–56, 2023) , 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. In Almiñana et al. (On heyting algebras with negative tense operators. Stud Logica 111:1015–1036, 2023), 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.