On the definition and the representability of quasi-polyadic equality algebras

摘要

We show that the usual axiom system of quasi polyadic equality algebras is strongly redundant. Then, so called non-commutative quasi-polyadic equality algebras are introduced (QPEN(alpha)), in which, among others, the commutativity of cylindrifications is dropped. As is known, quasi-polyadic equality algebras are not representable in the classical sense, but we prove that algebras in QPEN(alpha) are representable by quasi-polyadic relativized set algebras, or more exactly by algebras in Gwq(alpha). (C) 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim