JP Journal of Algebra, Number Theory and Applications
Volume 20, Issue 1, Pages 1 - 20
(February 2011)
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ON FINITE AXIOMATIZABILITY OF EXPANSIONS OF CYLINDRIC ALGEBRAS
Tarek Sayed Ahmed
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Abstract: We study expansions of (representable) cylindric algebras ?that are reducts of polyadic equality algebras. The question we address is: Can we add finitely many substitutions, so that in the expanded language of ?there is a finite set of quantifier free formulas that force representability of the cylindric reduct of algebras satisfying them. A refinement of a known positive solution (with a new proof) is presented. On the other hand, we show that if we expand the language of ?by finitely many substitutions corresponding to bijections, then in the expanded language, no quantifier free set of formulas containing only finitely many variables axiomatize |
Keywords and phrases: finite axiomatizability, cylindric algebras. |
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