Open Filters and Congruence Relations on Self-Distributive Weak Heyting Algebras

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Bulletin of the Section of Logic 53 (4):455-477 (2024)
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Abstract

In this paper, we study (open) filters and deductive systems of self-distributive weak Heyting algebras (SDWH-algebras) and obtain some results which determine the relationship between them. We show that the variety of SDWH-algebras is not weakly regular and every open filter is the kernel of at least one congruence relation. Finally, we characterize those SDWH-algebras which are weakly regular by using some properties involving principal congruence relations.

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10.18778/0138-0680.2024.13

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Basic Propositional Calculus I.Mohammad Ardeshir & Wim Ruitenburg - 1998 - Mathematical Logic Quarterly 44 (3):317-343.
Bounded distributive lattices with strict implication.Sergio Celani & Ramon Jansana - 2005 - Mathematical Logic Quarterly 51 (3):219-246.
Logics Which Are Characterized by Subresiduated Lattices.George Epstein & Alfred Horn - 1976 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 22 (1):199-210.

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