11 found
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  1.  15
    On Weak and Strong Interpolation in Algebraic Logics.Gábor Sági & Saharon Shelah - 2006 - Journal of Symbolic Logic 71 (1):104 - 118.
    We show that there is a restriction, or modification of the finite-variable fragments of First Order Logic in which a weak form of Craig's Interpolation Theorem holds but a strong form of this theorem does not hold. Translating these results into Algebraic Logic we obtain a finitely axiomatizable subvariety of finite dimensional Representable Cylindric Algebras that has the Strong Amalgamation Property but does not have the Superamalgamation Property. This settles a conjecture of Pigozzi [12].
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  2.  62
    A Completeness Theorem for Higher Order Logics.Gábor Sági - 2000 - Journal of Symbolic Logic 65 (2):857-884.
    Here we investigate the classes RCA $^\uparrow_\alpha$ of representable directed cylindric algebras of dimension α introduced by Nemeti[12]. RCA $^\uparrow_\alpha$ can be seen in two different ways: first, as an algebraic counterpart of higher order logics and second, as a cylindric algebraic analogue of Quasi-Projective Relation Algebras. We will give a new, "purely cylindric algebraic" proof for the following theorems of Nemeti: (i) RCA $^\uparrow_\alpha$ is a finitely axiomatizable variety whenever α ≥ 3 is finite and (ii) one can obtain (...)
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  3.  15
    On the Equational Theory of Representable Polyadic Equality Algebras.István Németi & Gábor Sági - 2000 - Journal of Symbolic Logic 65 (3):1143-1167.
    Among others we will prove that the equational theory of ω dimensional representable polyadic equality algebras (RPEA ω 's) is not schema axiomatizable. This result is in interesting contrast with the Daigneault-Monk representation theorem, which states that the class of representable polyadic algebras is finite schema-axiomatizable (and hence the equational theory of this class is finite schema-axiomatizable, as well). We will also show that the complexity of the equational theory of RPEA ω is also extremely high in the recursion theoretic (...)
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  4.  15
    A Note on Algebras of Substitutions.Gábor Sági - 2002 - Studia Logica 72 (2):265-284.
    We will study the class RSA of -dimensional representable substitution algebras. RSA is a sub-reduct of the class of representable cylindric: algebras, and it was an open problem in Andréka [1] that whether RSA can be finitely axiomatized. We will show, that the answer is positive. More concretely, we will prove, that RSA is a finitely axiomatizable quasi-variety. The generated variety is also described. We note that RSA is the algebraic counterpart of a certain proportional multimodal logic and it is (...)
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  5.  15
    Ultratopologies.Gábor Sági & János Gerlits - 2004 - Mathematical Logic Quarterly 50 (6):603-612.
    The notion of ultratopologies was introduced in [6] motivated by the model theory of first and higher order logics. In [6] we established some model theoretical applications of ultratopologies, for example, we provided a purely set theoretical characterization for classes de.nable by second order existential formulas. The present note deals with topological properties of ultratopologies, like density and compactness.
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  6.  15
    Ultraproducts and Higher Order Formulas.Gábor Sági - 2002 - Mathematical Logic Quarterly 48 (2):261-275.
    Which ultraproducts preserve the validity of formulas of higher order logics? To answer this question, we will introduce natural topologies on ultraproducts. We will show, that ultraproducts preserving certain higher order formulas can be characterized in terms of these topologies. As an application of the above results, we provide a constructive, purely model theoretic characterization for classes definable by second order existential formulas.
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  7.  18
    On Topological Properties of Ultraproducts of Finite Sets.Gábor Sági & Saharon Shelah - 2005 - Mathematical Logic Quarterly 51 (3):254-257.
    In [3] a certain family of topological spaces was introduced on ultraproducts. These spaces have been called ultratopologies and their definition was motivated by model theory of higher order logics. Ultratopologies provide a natural extra topological structure for ultraproducts. Using this extra structure in [3] some preservation and characterization theorems were obtained for higher order logics. The purely topological properties of ultratopologies seem interesting on their own right. We started to study these properties in [2], where some questions remained open. (...)
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  8.  1
    On the Equational Theory of Representable Polyadic Equality Algebras.Istvan Nemeti & Gabor Sagi - 2000 - Journal of Symbolic Logic 65 (3):1143-1167.
    Among others we will prove that the equational theory of $\omega$ dimensional representable polyadic equality algebras is not schema axiomatizable. This result is in interesting contrast with the Daigneault-Monk representation theorem, which states that the class of representable polyadic algebras is finite schema-axiomatizable. We will also show that the complexity of the equational theory of RPEA$_\omega$ is also extremely high in the recursion theoretic sense. Finally, comparing the present negative results with the positive results of Ildiko Sain and Viktor Gyuris (...)
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  9.  16
    Upward Morley's Theorem Downward.Gábor Sági & Zalán Gyenis - 2013 - Mathematical Logic Quarterly 59 (4-5):303-331.
  10.  11
    Absolutely Ubiquitous Structures and ℵ0-Stability.Gábor Sági - 2010 - Bulletin of the Section of Logic 39 (1/2):43-51.
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  11.  8
    A Short Proof for the Completeness of Paramodulacion.Gábor Sági - 2010 - Bulletin of the Section of Logic 39 (3/4):147-152.
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