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March 2008 Omitting types for finite variable fragments and complete representations of algebras
Tarek Sayed Ahmed, Hajnal Andréka, István Németi
J. Symbolic Logic 73(1): 65-89 (March 2008). DOI: 10.2178/jsl/1208358743

Abstract

We give a novel application of algebraic logic to first order logic. A new, flexible construction is presented for representable but not completely representable atomic relation and cylindric algebras of dimension n (for finite n≥2) with the additional property that they are one-generated and the set of all n by n atomic matrices forms a cylindric basis. We use this construction to show that the classical Henkin-Orey omitting types theorem fails for the finite variable fragments of first order logic as long as the number of variables available is ≥2 and we have a binary relation symbol in our language. We also prove a stronger result to the effect that there is no finite upper bound for the extra variables needed in the witness formulas. This result further emphasizes the ongoing interplay between algebraic logic and first order logic.

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Tarek Sayed Ahmed. Hajnal Andréka. István Németi. "Omitting types for finite variable fragments and complete representations of algebras." J. Symbolic Logic 73 (1) 65 - 89, March 2008. https://doi.org/10.2178/jsl/1208358743

Information

Published: March 2008
First available in Project Euclid: 16 April 2008

zbMATH: 1143.03035
MathSciNet: MR2387933
Digital Object Identifier: 10.2178/jsl/1208358743

Rights: Copyright © 2008 Association for Symbolic Logic

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Vol.73 • No. 1 • March 2008
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