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Martin's Axiom, Omitting Types, and Complete Representations in Algebraic Logic

Tarek Sayed Ahmed
Studia Logica: An International Journal for Symbolic Logic
Vol. 72, No. 2, Many-Dimensional Logical Systems (Nov., 2002), pp. 285-309
Published by: Springer
Stable URL: http://www.jstor.org/stable/20016465
Page Count: 25
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Martin's Axiom, Omitting Types, and Complete Representations in Algebraic Logic
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Abstract

We give a new characterization of the class of completely representable cylindric algebras of dimension 2 < n ≤ ω via special neat embeddings. We prove an independence result connecting cylindric algebra to Martin's axiom. Finally we apply our results to finite-variable first order logic showing that Henkin and Orey's omitting types theorem fails for $L_{n}$, the first order logic restricted to the first n variables when 2 < n < ω. $L_{n}$ has been recently (and quite extensively) studied as a many-dimensional modal logic.

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