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  1. On the Restraining Power of Guards.Erich Grädel - 1999 - Journal of Symbolic Logic 64 (4):1719-1742.
    Guarded fragments of first-order logic were recently introduced by Andreka, van Benthem and Nemeti; they consist of relational first-order formulae whose quantifiers are appropriately relativized by atoms. These fragments are interesting because they extend in a natural way many propositional modal logics, because they have useful model-theoretic properties and especially because they are decidable classes that avoid the usual syntactic restrictions of almost all other known decidable fragments of first-order logic. Here, we investigate the computational complexity of these fragments. We (...)
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  • On the Restraining Power of Guards.Erich Grädel - 1999 - Journal of Symbolic Logic 64 (4):1719-1742.
    Guarded fragments of first-order logic were recently introduced by Andreka, van Benthem and Nemeti; they consist of relational first-order formulae whose quantifiers are appropriately relativized by atoms. These fragments are interesting because they extend in a natural way many propositional modal logics, because they have useful model-theoretic properties and especially because they are decidable classes that avoid the usual syntactic restrictions (on the arity of relation symbols, the quantifier pattern or the number of variables) of almost all other known decidable (...)
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  • Some Aspects of Model Theory and Finite Structures.Eric Rosen - 2002 - Bulletin of Symbolic Logic 8 (3):380-403.
  • 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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