Martin's axiom, omitting types, and complete representations in algebraic logic

Studia Logica 72 (2):285 - 309 (2002)
We give a new characterization of the class of completely representable cylindric algebras of dimension 2 #lt; n w 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 #lt; n#lt;w. L n has been recently (and quite extensively) studied as a many-dimensional modal logic
Keywords Philosophy   Logic   Mathematical Logic and Foundations   Computational Linguistics
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