On complete representations of reducts of polyadic algebras (Q1005935)

By reducts of polyadic algebras the author means here the \(G\)-polyadic algebras already studied by him in [Algebra Univers. 51, No. 4, 301--359 (2004; Zbl 1126.03053)]. The main theorem of the present paper states that every abstract atomic and countable \(G\)-polyadic algebra, where \(G\) is a countable rich sub-semigroup of \(\omega^\omega\), admits representations that preserve infinite meets and joins. This contrasts with the cases of cylindric and relational algebras. (The countability is essential for the presented proof of the theorem.)