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Complete Theories

Journal of Symbolic Logic 25 (2):172-174 (1960)

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  1. Pseudo‐C‐Archimedean and Pseudo‐Finite Cyclically Ordered Groups.Gérard Leloup - 2019 - Mathematical Logic Quarterly 65 (4):412-443.
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  • The Role of Intuition in Gödel’s and Robinson’s Points of View.Talia Leven - 2019 - Axiomathes 29 (5):441-461.
    Before Abraham Robinson and Kurt Gödel became familiar with Paul Cohen’s Results, both logicians held a naïve Platonic approach to philosophy. In this paper I demonstrate how Cohen’s results influenced both of them. Robinson declared himself a Formalist, while Gödel basically continued to hold onto the old Platonic approach. Why were the reactions of Gödel and Robinson to Cohen’s results so drastically different in spite of the fact that their initial philosophical positions were remarkably similar? I claim that the key (...)
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  • On Stably Pointed Varieties and Generically Stable Groups in ACVF.Yatir Halevi - 2019 - Annals of Pure and Applied Logic 170 (2):180-217.
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  • On the Representation of Herbrand Functions in Algebraically Closed Fields.A. H. Lightstone & A. Robinson - 1957 - Journal of Symbolic Logic 22 (2):187-204.
  • Existentially Closed Algebras and Boolean Products.Herbert H. J. Riedel - 1988 - Journal of Symbolic Logic 53 (2):571-596.
    A Boolean product construction is used to give examples of existentially closed algebras in the universal Horn class ISP(K) generated by a universal class K of finitely subdirectly irreducible algebras such that Γ a (K) has the Fraser-Horn property. If $\lbrack a \neq b\rbrack \cap \lbrack c \neq d\rbrack = \varnothing$ is definable in K and K has a model companion of K-simple algebras, then it is shown that ISP(K) has a model companion. Conversely, a sufficient condition is given for (...)
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  • Some Forms of Completeness.P. C. Gilmore - 1962 - Journal of Symbolic Logic 27 (3):344-352.
  • Persistence and Herbrand Expansions.Joseph S. Wholey - 1963 - Journal of Symbolic Logic 28 (4):280-282.
  • Model Companions and K-Model Completeness for the Complete Theories of Boolean Algebras.J. Mead & G. C. Nelson - 1980 - Journal of Symbolic Logic 45 (1):47-55.
  • Ars inveniendi et théorie des modèles.Hourya Benis-Sinaceur - 1988 - Dialogue 27 (4):591-.
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  • Alfred Tarski's Elimination Theory for Real Closed Fields.Lou Van Den Dries - 1988 - Journal of Symbolic Logic 53 (1):7-19.
  • Canonical Forms for Definable Subsets of Algebraically Closed and Real Closed Valued Fields.Jan E. Holly - 1995 - Journal of Symbolic Logic 60 (3):843-860.
    We present a canonical form for definable subsets of algebraically closed valued fields by means of decompositions into sets of a simple form, and do the same for definable subsets of real closed valued fields. Both cases involve discs, forming "Swiss cheeses" in the algebraically closed case, and cuts in the real closed case. As a step in the development, we give a proof for the fact that in "most" valued fields F, if f(x),g(x) ∈ F[ x] and v is (...)
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  • Prototypes for Definable Subsets of Algebraically Closed Valued Fields.Jan E. Holly - 1997 - Journal of Symbolic Logic 62 (4):1093-1141.
    Elimination of imaginaries for 1-variable definable equivalence relations is proved for a theory of algebraically closed valued fields with new sorts for the disc spaces. The proof is constructive, and is based upon a new framework for proving elimination of imaginaries, in terms of prototypes which form a canonical family of formulas for defining each set that is definable with parameters. The proof also depends upon the formal development of the tree-like structure of valued fields, in terms of valued trees, (...)
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  • A Note on Valuation Definable Expansions of Fields.Deirdre Haskell & Dugald Macpherson - 1998 - Journal of Symbolic Logic 63 (2):739-743.
  • Relative Decidability and Definability in Henselian Valued Fields.Joseph Flenner - 2011 - Journal of Symbolic Logic 76 (4):1240-1260.
    Let (K, v) be a henselian valued field of characteristic 0. Then K admits a definable partition on each piece of which the leading term of a polynomial in one variable can be computed as a definable function of the leading term of a linear map. The main step in obtaining this partition is an answer to the question, given a polynomial f(x) ∈ K[x], what is v(f(x))? Two applications are given: first, a constructive quantifier elimination relative to the leading (...)
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  • Stable Embeddedness in Algebraically Closed Valued Fields.E. Hrushovski & A. Tatarsky - 2006 - Journal of Symbolic Logic 71 (3):831 - 862.
    We give some general criteria for the stable embeddedness of a definable set. We use these criteria to establish the stable embeddedness in algebraically closed valued fields of two definable sets: The set of balls of a given radius r < 1 contained in the valuation ring and the set of balls of a given multiplicative radius r < 1. We also show that in an algebraically closed valued field a 0-definable set is stably embedded if and only if its (...)
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  • Strongly Minimal Reducts of Valued Fields.Piotr Kowalski & Serge Randriambololona - 2016 - Journal of Symbolic Logic 81 (2):510-523.
  • Sheaves and Boolean Valued Model Theory.George Loullis - 1979 - Journal of Symbolic Logic 44 (2):153-183.
  • The Lω1ω1-Theory of Hilbert Spaces.Ralph Kopperman - 1967 - Journal of Symbolic Logic 32 (3):295 - 304.
  • Further Results on Infinite Valued Predicate Logic.L. P. Belluce - 1964 - Journal of Symbolic Logic 29 (2):69-78.
  • Positive Jonsson Theories.Bruno Poizat & Aibat Yeshkeyev - 2018 - Logica Universalis 12 (1-2):101-127.
    This paper is a general introduction to Positive Logic, where only what we call h-inductive sentences are under consideration, allowing the extension to homomorphisms of model-theoric notions which are classically associated to embeddings; in particular, the existentially closed models, that were primitively defined by Abraham Robinson, become here positively closed models. It accounts for recent results in this domain, and is oriented towards the positivisation of Jonsson theories.
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  • The Theory of Affine Constructible Sets.Williams Kramer Forrest - 1983 - Mathematical Logic Quarterly 29 (3):97-135.
  • Élimination Des Quantificateurs Dans Des Paires de Corps.G. Leloup - 1995 - Journal of Symbolic Logic 60 (2):548-562.
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  • Model Completeness and Direct Power.Kazem Taghva - 1990 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 36 (1):3-9.