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On the complexity of axiomatizations of the class of representable quasi‐polyadic equality algebras
Author(s) -
Ahmed Tarek Sayed
Publication year - 2011
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.201010015
Subject(s) - mathematics , class (philosophy) , permutation (music) , diagonal , dimension (graph theory) , algebraic number , omega , combinatorics , algebra over a field , pure mathematics , mathematical analysis , physics , geometry , quantum mechanics , computer science , artificial intelligence , acoustics
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 Andréka’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 \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$2< n <\omega$\end{document} and \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$l< n,$\end{document} \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$k < n$\end{document} , 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. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim