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  1. Algebraic Logic, Where Does It Stand Today?Tarek Sayed Ahmed - 2005 - Bulletin of Symbolic Logic 11 (3):465-516.
    This is a survey article on algebraic logic. It gives a historical background leading up to a modern perspective. Central problems in algebraic logic (like the representation problem) are discussed in connection to other branches of logic, like modal logic, proof theory, model-theoretic forcing, finite combinatorics, and Gödel’s incompleteness results. We focus on cylindric algebras. Relation algebras and polyadic algebras are mostly covered only insofar as they relate to cylindric algebras, and even there we have not told the whole story. (...)
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  • Neat Embeddings, Omitting Types, and Interpolation: An Overview.Tarek Sayed Ahmed - 2003 - Notre Dame Journal of Formal Logic 44 (3):157-173.
    We survey various results on the relationship among neat embeddings (a notion special to cylindric algebras), complete representations, omitting types, and amalgamation. A hitherto unpublished application of algebraic logic to omitting types of first-order logic is given.
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  • 1996 European Summer Meeting of the Association for Symbolic Logic.G. Mints, M. Otero, S. Ronchi Della Rocca & K. Segerberg - 1997 - Bulletin of Symbolic Logic 3 (2):242-277.
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  • 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.
    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 (...)
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  • 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.
    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 (...)
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  • 1996 European Summer Meeting of the Association for Symbolic Logic.Daniel Lascar - 1997 - Bulletin of Symbolic Logic 3 (2):242-277.
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  • On neat reducts of algebras of logic.Tarek Sayed Ahmed & Istvan Németi - 2001 - Studia Logica 68 (2):229-262.
    SC , CA , QA and QEA stand for the classes of Pinter's substitution algebras, Tarski's cylindric algebras, Halmos' quasipolyadic algebras, and quasipolyadic equality algebras of dimension , respectively. Generalizing a result of Németi on cylindric algebras, we show that for K {SC, CA, QA, QEA} and ordinals , the class Nr K of -dimensional neat reducts of -dimensional K algebras, though closed under taking homomorphic images and products, is not closed under forming subalgebras (i.e. is not a variety) if (...)
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  • A Note on Neat Reducts.Tarek Sayed Ahmed - 2007 - Studia Logica 85 (2):139-151.
    SC, CA, QA and QEA denote the class of Pinter’s substitution algebras, Tarski’s cylindric algebras, Halmos’ quasi-polyadic and quasi-polyadic equality algebras, respectively. Let . and . We show that the class of n dimensional neat reducts of algebras in K m is not elementary. This solves a problem in [2]. Also our result generalizes results proved in [1] and [2].
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  • A Modeltheoretic Solution to a Problem of Tarski.Tarek Sayed Ahmed - 2002 - Mathematical Logic Quarterly 48 (3):343-355.
    Let 1 n. We show that the class NrnCAβ of n-dimensional neat reducts of β-dimensional cylindric algebras is not closed under forming elementary subalgebras. This solves a long-standing open problem of Tarski and his co-authors Andréka, Henkin, Monk and Németi. The proof uses genuine model-theoretic arguments.
     
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