Double Equivalential Algebras

Abstract

In this paper, we introduce the notion of double equivalential algebras, defined as subreducts of double Heyting algebras with respect to the equivalence and dual equivalence operations. We establish the fundamental properties of these structures and investigate several distinguished classes related to them, including the class of double equivalential subreducts of Boolean algebras and the variety generated by the three-element chain, which is shown to be semisimple.