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

Summary/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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