On the complexity of axiomatizations of the class of representable quasi-polyadic equality algebras

摘要

Using games, as introduced by Hirsch and Hodkinson in algebraic logic, we give a recursive axiomatization of the class RQPEA_α of representable quasi-polyadic equality algebras of any dimension α. Following Sain and Thompson in modifying Andreka’s methods of splitting, to adapt the quasi-polyadic equality case, we show that if Σ is a set of equations axiomatizing RPEA_n for 2 < n < ω and l < n, k < n, k- < ω are natural numbers, then Σ contains infinitely equations in which occurs, one of + or · occurs, a diagonal or a permutation with index l occurs, more than k cylindrifications and more than k-variables occur.