26 found
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  1.  75
    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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  2.  56
    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.
    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 (...)
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  3.  50
    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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  4.  40
    Martin's Axiom, Omitting Types, and Complete Representations in Algebraic Logic.Tarek Sayed Ahmed - 2002 - Studia Logica 72 (2):285 - 309.
    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 (...)
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  5.  12
    The Neat Embedding Problem for Algebras Other Than Cylindric Algebras and for Infinite Dimensions.Robin Hirsch & Tarek Sayed Ahmed - 2014 - Journal of Symbolic Logic 79 (1):208-222.
  6.  32
    On Amalgamation in Algebras of Logic.Tarek Sayed Ahmed - 2005 - Studia Logica 81 (1):61-77.
    We show that not all epimorphisms are surjective in certain classes of infinite dimensional cylindric algebras, Pinter's substitution algebras and Halmos' quasipolyadic algebras with and without equality. It follows that these classes fail to have the strong amalgamation property. This answers a question in [3] and a question of Pigozzi in his landmark paper on amalgamation [9]. The cylindric case was first proved by Judit Madarasz [7]. The proof presented herein is substantially different. By a result of Németi, our result (...)
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  7.  16
    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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  8.  14
    An Omitting Types Theorem for First Order Logic with Infinitary Relation Symbols.Tarek Sayed Ahmed & Basim Samir - 2007 - Mathematical Logic Quarterly 53 (6):564-570.
    In this paper, an extension of first order logic is introduced. In such logics atomic formulas may have infinite lengths. An Omitting Types Theorem is proved.
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  9.  29
    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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  10.  15
    A Note on Substitutions in Representable Cylindric Algebras.Tarek Sayed Ahmed - 2009 - Mathematical Logic Quarterly 55 (3):280-287.
    We show that it is impossible to define a substitution operator for arbitrary representable cylindric algebras that agrees in its basic properties with the notion of substitutions introduced for dimension complemented algebras.
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  11.  9
    Varying Interpolation and Amalgamation in Polyadic MV-Algebras.Tarek Sayed Ahmed - 2015 - Journal of Applied Non-Classical Logics 25 (2):140-192.
    We prove several interpolation theorems for many-valued infinitary logic with quantifiers by studying expansions of MV-algebras in the spirit of polyadic and cylindric algebras. We prove for various reducts of polyadic MV-algebras of infinite dimensions that if is the free algebra in the given signature,, is in the subalgebra of generated by, is in the subalgebra of generated by and, then there exists an interpolant in the subalgebra generated by and such that. We call this a varying interpolation property because (...)
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  12.  35
    An Independence Result in Algebraic Logic.Tarek Sayed Ahmed - 2005 - Bulletin of the Section of Logic 34 (1):29-36.
  13.  29
    Neat Embeddings and Amalgamation.Tarek Sayed Ahmed & Basim Samir - 2006 - Bulletin of the Section of Logic 35 (4):163-171.
  14.  23
    Algebras of Sentences.Tarek Sayed Ahmed - 2006 - Bulletin of the Section of Logic 35 (1):1-10.
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  15.  22
    Amalgamation for Reducts of Polyadic Equality Algebras, a Negative Result.Tarek Sayed Ahmed - 2008 - Bulletin of the Section of Logic 37 (1):37-50.
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  16.  21
    The Class of Neat Reducts is Not Boolean Closed.Tarek Sayed Ahmed - 2008 - Bulletin of the Section of Logic 37 (1):51-61.
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  17.  20
    A Sufficient and Necessary Condition for Omitting Types.Tarek Sayed Ahmed - 2005 - Bulletin of the Section of Logic 34 (1):23-27.
  18.  20
    Racan is Not Elementary, for N≥ 5.Tarek Sayed Ahmed - 2008 - Bulletin of the Section of Logic 37 (2):123-136.
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  19.  21
    On a Theorem of Vaught for First Order Logic with Finitely Many Variables.Tarek Sayed Ahmed - 2009 - Journal of Applied Non-Classical Logics 19 (1):97-112.
    We prove that the existence of atomic models for countable atomic theories does not hold for Ln the first order logic restricted to n variables for finite n > 2. Our proof is algebraic, via polyadic algebras. We note that Lnhas been studied in recent times as a multi-modal logic with applications in computer science. 2000 MATHEMATICS SUBJECT CLASSIFICATION. 03C07, 03G15.
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  20.  17
    Classes of Algebras That Are Not Closed Under Completions.Mohamed Khaled & Tarek Sayed Ahmed - 2009 - Bulletin of the Section of Logic 38 (1/2):29-43.
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  21.  18
    A Non-Finitizability Result in Algebraic Logic.Tarek Sayed Ahmed - 2007 - Bulletin of the Section of Logic 36 (1/2):21-27.
  22.  15
    A Simple Construction of Representable Relation Algebras with Non‐Representable Completions.Tarek Sayed Ahmed - 2009 - Mathematical Logic Quarterly 55 (3):237-244.
    We give a simple new construction of representable relation algebras with non-representable completions. Using variations on our construction, we show that the elementary closure of the class of completely representable relation algebras is not finitely axiomatizable.
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  23.  16
    Classes of Representable Algebras with the Amalgamation Property.Tarek Sayed Ahmed - 2008 - Bulletin of the Section of Logic 37 (2):115-121.
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  24.  4
    Atom-Canonicity in Varieties of Cylindric Algebras with Applications to Omitting Types in Multi-Modal Logic.Tarek Sayed Ahmed - 2020 - Journal of Applied Non-Classical Logics 30 (3):223-271.
    Fix 2 < n < ω and let C A n denote the class of cylindric algebras of dimension n. Roughly, C A n is the algebraic counterpart of the proof theory of first-order logic restricted to the first n var...
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  25.  10
    A Simple Construction of Representable Relation Algebras with Non-Representable Completions.Tarek Sayed Ahmed - 2009 - Mathematical Logic Quarterly 55 (3):237-244.
    We give a simple new construction of representable relation algebras with non-representable completions. Using variations on our construction, we show that the elementary closure of the class of completely representable relation algebras is not finitely axiomatizable.
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  26.  8
    On Neat Embeddings of Cylindric Algebras.Tarek Sayed Ahmed - 2009 - Mathematical Logic Quarterly 55 (6):666-668.