Abstract
Let a be an infinite ordinal. Let RCA(alpha) denote the variety of representable cylindric algebras of dimension alpha. Modifying Andreka's methods of splitting, we show that the variety RQEA(alpha) of representable quasi-polyadic equality algebras of dimension alpha is not axiomatized by a set of universal formulas containing only finitely many variables over the variety RQA(alpha) of representable quasi-polyadic algebras of dimension alpha. This strengthens a seminal result due to Sain and Thompson, answers a question posed by Andreka, and lifts to the transfinite a result of hers proved for finite dimensions > 2. Using the modified method of splitting, we show that all known complexity results on universal axiomatizations of RCA(alpha) (proved by Andreka) transfer to universal axiomatizations of RQEA(alpha). From such results it can be inferred that any algebraizable extension of L-omega,L-omega is severely incomplete if we insist on Tarskian square semantics. Ways of circumventing the strong non-negative axiomatizability results hitherto obtained in the first part of the paper, such as guarding semantics, and/or expanding the signature of RQEA(omega) by substitutions indexed by transformations coming from a finitely presented subsemigroup of ((omega)omega,o) containing all transpositions and replacements, are surveyed, discussed, and elaborated upon.