On Heyting Algebras with Negative Tense Operators

Characterization of Subdirectly Irreducible Heyting Algebras with Negative Tense Operators

“…In this section, we will revisit the definition of tense H-algebras from [1]. Additionally, we will present the necessary definitions and results to facilitate a topological investigation of this variety.…”

“…In [1], it was proved that Definition 1 is equivalent to Definition 2. Therefore, in this paper, we will adopt the terminology established in [1].…”

“…In this section, our primary goal is to characterize the congruence lattice on a tense H-algebra using specific closed and increasing subsets of its associated tense H-space. For this purpose, it will be necessary to revisit definitions and findings regarding the Esakia duality for tense H-algebras (for further details, refer to [1]).…”

“…In [1], we proved that the category tHS, comprising tense H-spaces as objects and tense H-functions as morphisms, is dually equivalent to the category of tHA, which consists of tense H-algebras and tense H-homomorphisms.…”

“…In [1], we introduced the notion of negative tense operators on Heyting algebras and proved that this new class of algebras serves as the algebraic semantics of IGN. In this paper, we continue our investigation into negative tense operators on Heyting algebras, specifically focusing on their topological properties.…”