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

✍ Scribed by Tarek Sayed Ahmed

Publisher: John Wiley and Sons
Year: 2011
Tongue: English
Weight: 157 KB
Volume: 57
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.201010015

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✦ Synopsis

MSC (2010) Primary: 03G15

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 RPEAn for 2 < n < ω and l < n, k < n, k < ω are natural numbers, then Σ contains infinitely equations in whichoccurs, one of + or • occurs, a diagonal or a permutation with index l occurs, more than k cylindrifications and more than k variables occur.

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