On nonrepresentable G-polyadic algebras with representable cylindric reducts.

In [10], Sayed Ahmed recently has shown that there exists an infinite dimensional non-representable quasi-polyadic equality algebra (QPEAω, for short) with a representable cylindric reduct. In this paper we continue related investigations and show that if G⊆ωω is a semigroup containing at least one constant function, then a wide class of representable cylindric algebras occur as the cylindric reduct of some non-representable G-PEAω. More concretely, we prove that if A is an ω-dimensional cylindric set algebra with an infinite base set, then there exists a non-representable G-PEAω whose cylindric reduct is representable and contains an isomorphic copy of A. [ABSTRACT FROM PUBLISHER]