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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 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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Correspondence to Sándor Jenei.

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Jenei, S. Equality Algebras. Stud Logica 100, 1201–1209 (2012).

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  • BCK-algebra with meet
  • Equivalential fragment
  • Heyting algebra
  • Equivalential algebra
  • Closure operator
  • Term equivalence
  • Equational characterization