Abstract
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 result, which is analogous to a result of Kabziński and Wroński: we provide an equational characterization for the equivalential fragment of BCK-algebras with meet.
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Jenei, S. Equality Algebras. Stud Logica 100, 1201–1209 (2012). https://doi.org/10.1007/s11225-012-9457-0
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DOI: https://doi.org/10.1007/s11225-012-9457-0