Pseudo equality algebras |
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Authors: | Sándor Jenei László Kóródi |
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Institution: | 1. Institute of Mathematics and Informatics, University of Pécs, Ifjúság u. 6, 7624, Pecs, Hungary 2. Department of Knowledge-Based Mathematical Systems, Johannes Kepler University, 4040, Linz, Austria
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Abstract: | A new structure, called pseudo equality algebras, will be introduced. It has a constant and three connectives: a meet operation and two equivalences. A closure operator will be introduced in the class of pseudo equality algebras; we call the closed algebras equivalential. We show that equivalential pseudo equality algebras are term equivalent with pseudo BCK-meet-semilattices. As a by-product we obtain a general result, which is analogous to a result of Kabziński and Wroński: we provide an equational characterization for the equivalence operations of pseudo BCK-meet-semilattices. Our result treats a much more general algebraic structure, namely, pseudo BCK-meet-semilattice instead of Heyting algebras, on the other hand, we also need to use the meet operation. Finally, we prove that the variety of pseudo equality algebras is a subtractive, 1-regular, arithmetical variety. |
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