Equality Algebras

A new structure, called equality algebras, will be introduced. It has two connectives, a meet operation and an equivalence, and a constant. A closure operator will be defined in the class of equality algebras, and we call the closed algebras equivalential. We show that equivalential equality algebras are term equivalent with BCK-algebras with meet. As a by-product, we obtain a quite general generalization of a result of Kabzin ́ski and Wron ́ski: we provide an equational characterization for the equivalential fragment of BCK-algebras with meet.