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Neat Embeddings, Omitting Types, and Interpolation: An Overview

Tarek Sayed Ahmed

Notre Dame Journal of Formal Logic 44 (3):157-173 (2003)

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Omitting types for finite variable fragments and complete representations of algebras.Hajnal Andréka, István Németi & Tarek Sayed Ahmed - 2008 - Journal of Symbolic Logic 73 (1):65-89.details 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 (...) Download Export citation Bookmark 13 citations
Neat reducts and amalgamation in retrospect, a survey of results and some methods Part II: Results on amalgamation.Judit Madarász & Tarek Ahmed - 2009 - Logic Journal of the IGPL 17 (6):755-802.details Introduced by Leon Henkin back in the fifties, the notion of neat reducts is an old venerable notion in algebraic logic. But it is often the case that an unexpected viewpoint yields new insights. Indeed, the repercussions of the fact that the class of neat reducts is not closed under forming subalgebras turn out to be enormous. In this paper we review and, in the process, discuss, some of these repercussions in connection with the algebraic notion of amalgamation. Some new (...) Download Export citation Bookmark 4 citations
Polyadic and cylindric algebras of sentences.Mohamed Amer & Tarek Sayed Ahmed - 2006 - Mathematical Logic Quarterly 52 (5):444-449.details In this note we give an interpretation of cylindric algebras as algebras of sentences of first order logic. We show that the isomorphism types of such algebras of sentences coincide with the class of neat reducts of cylindric algebras. Also we show how this interpretation sheds light on some recent results. This is done by likening Henkin's Neat Embedding Theorem to his celebrated completeness proof. Download Export citation Bookmark 1 citation
Neat reducts and amalgamation in retrospect, a survey of results and some methods Part I: Results on neat reducts.Judit Madarász & Tarek Ahmed - 2009 - Logic Journal of the IGPL 17 (4):429-483.details Introduced by Leon Henkin back in the fifties, the notion of neat reducts is an old venerable notion in algebraic logic. But it is often the case that an unexpected viewpoint yields new insights. Indeed, the repercussions of the fact that the class of neat reducts is not closed under forming subalgebras turn out to be enormous. In this paper we review and, in the process, discuss, some of these repercussions in connection with the algebraic notion of amalgamation. Some new (...) Download Export citation Bookmark

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