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  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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  • Three Interpolation Theorems for Typeless Logics.T. Sayed Ahmed - 2012 - Logic Journal of the IGPL 20 (6):1001-1037.
  • 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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  • 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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  • The Robinson Property and Amalgamations of Higher Arities.David Nyiri - 2016 - Mathematical Logic Quarterly 62 (4-5):427-433.
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  • Neat Embeddings as Adjoint Situations.Tarek Sayed-Ahmed - 2015 - Synthese 192 (7):1-37.
    Looking at the operation of forming neat $\alpha $ -reducts as a functor, with $\alpha $ an infinite ordinal, we investigate when such a functor obtained by truncating $\omega $ dimensions, has a right adjoint. We show that the neat reduct functor for representable cylindric algebras does not have a right adjoint, while that of polyadic algebras is an equivalence. We relate this categorial result to several amalgamation properties for classes of representable algebras. We show that the variety of cylindric (...)
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  • Interpolation Property and Homogeneous Structures.Z. Gyenis - 2014 - Logic Journal of the IGPL 22 (4):597-607.