27 found
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  1.  23
    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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  2.  21
    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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  3.  19
    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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  4.  30
    An Independence Result in Algebraic Logic.Tarek Sayed Ahmed - 2005 - Bulletin of the Section of Logic 34 (1):29-36.
  5.  2
    The Class of Polyadic Algebras has the Super Amalgamation Property.Tarek Sayed Ahmed - 2010 - Mathematical Logic Quarterly 56 (1):103-112.
    We show that for infinite ordinals α the class of polyadic algebras of dimension α has the super amalgamation property.
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  6.  1
    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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  7.  20
    Neat Embeddings and Amalgamation.Tarek Sayed Ahmed & Basim Samir - 2006 - Bulletin of the Section of Logic 35 (4):163-171.
  8.  16
    A Sufficient and Necessary Condition for Omitting Types.Tarek Sayed Ahmed - 2005 - Bulletin of the Section of Logic 34 (1):23-27.
  9.  2
    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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  10.  14
    Algebras of Sentences.Tarek Sayed Ahmed - 2006 - Bulletin of the Section of Logic 35 (1):1-10.
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  11.  14
    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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  12.  14
    The Class of Neat Reducts is Not Boolean Closed.Tarek Sayed Ahmed - 2008 - Bulletin of the Section of Logic 37 (1):51-61.
  13.  10
    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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  14.  11
    A Non-Finitizability Result in Algebraic Logic.Tarek Sayed Ahmed - 2007 - Bulletin of the Section of Logic 36 (1/2):21-27.
  15.  9
    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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  16.  6
    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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  17.  18
    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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  18.  3
    On the Complexity of Axiomatizations of the Class of Representable Quasi‐Polyadic Equality Algebras.Tarek Sayed Ahmed - 2011 - Mathematical Logic Quarterly 57 (4):384-394.
    Using games, as introduced by Hirsch and Hodkinson in algebraic logic, we give a recursive axiomatization of the class RQPEAα of representable quasi-polyadic equality algebras of any dimension α. Following Sain and Thompson in modifying Andréka’s methods of splitting, to adapt the quasi-polyadic equality case, we show that if Σ is a set of equations axiomatizing RPEAn for equation image and equation imageequation image, k′ < ω are natural numbers, then Σ contains infinitely equations in which − occurs, one of (...)
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  19.  2
    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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  20.  2
    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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  21.  2
    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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  22.  6
    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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  23.  3
    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.
  24.  2
    On Neat Embeddings of Cylindric Algebras.Tarek Sayed Ahmed - 2009 - Mathematical Logic Quarterly 55 (6):666-668.
  25.  1
    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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  26.  1
    Weakly Representable Atom Structures That Are Not Strongly Representable, with an Application to First Order Logic.Tarek Sayed Ahmed - 2008 - Mathematical Logic Quarterly 54 (3):294-306.
    Letn > 2. A weakly representable relation algebra that is not strongly representable is constructed. It is proved that the set of all n by n basic matrices forms a cylindric basis that is also a weakly but not a strongly representable atom structure. This gives an example of a binary generated atomic representable cylindric algebra with no complete representation. An application to first order logic is given.
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  27. 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.