26 found
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  1.  31
    A New Strongly Minimal Set.Ehud Hrushovski - 1993 - Annals of Pure and Applied Logic 62 (2):147-166.
    We construct a new class of 1 categorical structures, disproving Zilber's conjecture, and study some of their properties.
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  2.  7
    Unidimensional Theories Are Superstable.Ehud Hrushovski - 1990 - Annals of Pure and Applied Logic 50 (2):117-137.
    A first order theory T of power λ is called unidimensional if any twoλ+-saturated models of T of the same cardinality are isomorphic. We prove here that such theories are superstable, solving a problem of Shelah. The proof involves an existence theorem and a definability theorem for definable groups in stable theories, and an analysis of their relation to regular types.
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  3.  9
    The Manin–Mumford Conjecture and the Model Theory of Difference Fields.Ehud Hrushovski - 2001 - Annals of Pure and Applied Logic 112 (1):43-115.
    Using methods of geometric stability , we determine the structure of Abelian groups definable in ACFA, the model companion of fields with an automorphism. We also give general bounds on sets definable in ACFA. We show that these tools can be used to study torsion points on Abelian varieties; among other results, we deduce a fairly general case of a conjecture of Tate and Voloch on p-adic distances of torsion points from subvarieties.
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  4.  6
    Almost Orthogonal Regular Types.Ehud Hrushovski - 1989 - Annals of Pure and Applied Logic 45 (2):139-155.
  5.  4
    A Dichotomy Theorem for Regular Types.Ehud Hrushovski & Saharon Shelah - 1989 - Annals of Pure and Applied Logic 45 (2):157-169.
  6.  33
    On Pseudo-Finite Dimensions.Ehud Hrushovski - 2013 - Notre Dame Journal of Formal Logic 54 (3-4):463-495.
    We attempt to formulate issues around modularity and Zilber’s trichotomy in a setting that intersects additive combinatorics. In particular, we update the open problems on quasi-finite structures from [9].
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  7.  18
    Kueker's Conjecture for Stable Theories.Ehud Hrushovski - 1989 - Journal of Symbolic Logic 54 (1):207-220.
    Kueker's conjecture is proved for stable theories, for theories that interpret a linear ordering, and for theories with Skolem functions. The proof of the stable case involves certain results on coordinatization that are of independent interest.
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  8.  32
    A Note on Generically Stable Measures and Fsg Groups.Ehud Hrushovski, Anand Pillay & Pierre Simon - 2012 - Notre Dame Journal of Formal Logic 53 (4):599-605.
    We prove (Proposition 2.1) that if $\mu$ is a generically stable measure in an NIP (no independence property) theory, and $\mu(\phi(x,b))=0$ for all $b$ , then for some $n$ , $\mu^{(n)}(\exists y(\phi(x_{1},y)\wedge \cdots \wedge\phi(x_{n},y)))=0$ . As a consequence we show (Proposition 3.2) that if $G$ is a definable group with fsg (finitely satisfiable generics) in an NIP theory, and $X$ is a definable subset of $G$ , then $X$ is generic if and only if every translate of $X$ does not (...)
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  9.  8
    On the Automorphism Groups of Finite Covers.David M. Evans & Ehud Hrushovski - 1993 - Annals of Pure and Applied Logic 62 (2):83-112.
    We are concerned with identifying by how much a finite cover of an 0-categorical structure differs from a sequence of free covers. The main results show that this is measured by automorphism groups which are nilpotent-by-abelian. In the language of covers, these results say that every finite cover can be decomposed naturally into linked, superlinked and free covers. The superlinked covers arise from covers over a different base, and to describe this properly we introduce the notion of a quasi-cover.These results (...)
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  10.  20
    Finitely Based Theories.Ehud Hrushovski - 1989 - Journal of Symbolic Logic 54 (1):221-225.
    A stable theory is finitely based if every set of indiscernibles is based on a finite subset. This is a common generalization of superstability and 1-basedness. We show that if such theories have more than one model they must have infinitely many, and prove some other conjectures.
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  11.  47
    La Limite Des Theories de Courbes Generiques.Olivier Chapuis, Ehud Hrushovski, Pascal Koiran & Bruno Poizat - 2002 - Journal of Symbolic Logic 67 (1):24-34.
    Ne estas prima orda formulo, kiu definas la Zariskijajn slositojn inter la konstruitoj, malpli ke la konektojn inter la slositoj.
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  12.  17
    A Question of Van Den Dries and a Theorem of Lipshitz and Robinson; Not Everything Is Standard.Ehud Hrushovski & Ya'acov Peterzil - 2007 - Journal of Symbolic Logic 72 (1):119 - 122.
    We use a new construction of an o-minimal structure, due to Lipshitz and Robinson, to answer a question of van den Dries regarding the relationship between arbitrary o-minimal expansions of real closed fields and structures over the real numbers. We write a first order sentence which is true in the Lipshitz-Robinson structure but fails in any possible interpretation over the field of real numbers.
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  13.  11
    Finitely Axiomatizable ℵ1 Categorical Theories.Ehud Hrushovski - 1994 - Journal of Symbolic Logic 59 (3):838 - 844.
    Finitely axiomatizable ℵ 1 categorical theories are locally modular.
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  14.  29
    DMP in Strongly Minimal Sets.Assaf Hasson & Ehud Hrushovski - 2007 - Journal of Symbolic Logic 72 (3):1019 - 1030.
    We construct a strongly minimal set which is not a finite cover of one with DMP. We also show that for a strongly minimal theory T, generic automorphisms exist iff T has DMP, thus proving a conjecture of Kikyo and Pillay.
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  15.  26
    Strongly and Co-Strongly Minimal Abelian Structures.Ehud Hrushovski & James Loveys - 2010 - Journal of Symbolic Logic 75 (2):442-458.
    We give several characterizations of weakly minimal abelian structures. In two special cases, dual in a sense to be made explicit below, we give precise structure theorems: 1. When the only finite 0-definable subgroup is {0}, or equivalently 0 is the only algebraic element (the co-strongly minimal case); 2. When the theory of the structure is strongly minimal. In the first case, we identify the abelian structure as a "near-subspace" A of a vector space V over a division ring D (...)
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  16.  9
    [Omnibus Review].Ehud Hrushovski - 1993 - Journal of Symbolic Logic 58 (2):710-713.
    Reviewed Works:B. I. Zil'ber, L. Pacholski, J. Wierzejewski, A. J. Wilkie, Totally Categorical Theories: Structural Properties and the Non-Finite Axiomatizability.B. I. Zil'ber, Strongly Minimal Countably Categorical Theories.B. I. Zil'ber, Strongly Minimal Countably Categorical Theories. II.B. I. Zil'ber, Strongly Minimal Countably Categorical Theories. III.B. I. Zil'ber, E. Mendelson, Totally Categorical Structures and Combinatorial Geometries.B. I. Zil'ber, The Structure of Models of Uncountably Categorical Theories.
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  17.  14
    Unique Decomposition in Classifiable Theories.Bradd Hart, Ehud Hrushovski & Michael C. Laskowski - 2002 - Journal of Symbolic Logic 67 (1):61-68.
  18.  13
    A Note on Orthogonality and Stable Embeddedness.Gregory Cherlin, Marko Djordjevic & Ehud Hrushovski - 2005 - Journal of Symbolic Logic 70 (4):1359 - 1364.
    Orthogonality between two stably embedded definable sets is preserved under the addition of constants.
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  19.  5
    Generalizations of Kochen and Specker's Theorem and the Effectiveness of Gleason's Theorem.Ehud Hrushovski & Itamar Pitowsky - 2004 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 35 (2):177-194.
    Kochen and Specker's theorem can be seen as a consequence of Gleason's theorem and logical compactness. Similar compactness arguments lead to stronger results about finite sets of rays in Hilbert space, which we also prove by a direct construction. Finally, we demonstrate that Gleason's theorem itself has a constructive proof, based on a generic, finite, effectively generated set of rays, on which every quantum state can be approximated.
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  20.  6
    Unexpected Imaginaries in Valued Fields with Analytic Structure.Deirdre Haskell, Ehud Hrushovski & Dugald Macpherson - 2013 - Journal of Symbolic Logic 78 (2):523-542.
    We give an example of an imaginary defined in certain valued fields with analytic structure which cannot be coded in the ‘geometric' sorts which suffice to code all imaginaries in the corresponding algebraic setting.
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  21.  7
    On Algebraic Closure in Pseudofinite Fields.Özlem Beyarslan & Ehud Hrushovski - 2012 - Journal of Symbolic Logic 77 (4):1057-1066.
    We study the automorphism group of the algebraic closure of a substructure A of a pseudofinite field F. We show that the behavior of this group, even when A is large, depends essentially on the roots of unity in F. For almost all completions of the theory of pseudofinite fields, we show that over A, algebraic closure agrees with definable closure, as soon as A contains the relative algebraic closure of the prime field.
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  22.  3
    Zil′Ber B. I.. Totally Categorical Theories: Structural Properties and the Non-Finite Axiomatizability. Model Theory of Algebra and Arithmetic, Proceedings of the Conference on Applications of Logic to Algebra and Arithmetic Held at Karpacz, Poland, September 1–7, 1979, Edited by L. Pacholski, J. Wierzejewski, and A. J. Wilkie, Lecture Notes in Mathematics, Vol. 834, Springer-Verlag, Berlin, Heidelberg, and New York, 1980, Pp. 381–410.Zil′Ber B. I.. Strongly Minimal Countably Categorical Theories. Siberian Mathematical Journal, Vol. 21 No. 2 , Pp. 219–230. , Pp. 98-112.)Zil′Ber B. I.. Strongly Minimal Countably Categorical Theories. II. Ibid., Vol. 25 No. 3 , Pp. 396-412. , Pp. 71-88.)Zil′Ber B. I.. Strongly Minimal Countably Categorical Theories. III. Ibid., Vol. 25 No. 4 , Pp. 559-571. , Pp. 63-77.)Zil′Ber B. I.. Totally Categorical Structures and Combinatorial Geometries. Soviet Mathematics–Doklady, Vol. 24 No. 1 , Pp. 149-151. , Pp. 1039-1041.)Zil′Ber B. I. The Structure of Models. [REVIEW]Ehud Hrushovski - 1993 - Journal of Symbolic Logic 58 (2):710-713.
  23.  9
    Lascar and Morley Ranks Differ in Differentially Closed Fields.Ehud Hrushovski & Thomas Scanlon - 1999 - Journal of Symbolic Logic 64 (3):1280-1284.
  24.  2
    Lascar and Morley Ranks Differ in Differentially Closed Fields.Ehud Hrushovski & Thomas Scanlon - 1999 - Journal of Symbolic Logic 64 (3):1280-1284.
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  25.  3
    Classifiable Theories Without Finitary Invariants.Elisabeth Bouscaren & Ehud Hrushovski - 2006 - Annals of Pure and Applied Logic 142 (1):296-320.
    It follows directly from Shelah’s structure theory that if T is a classifiable theory, then the isomorphism type of any model of T is determined by the theory of that model in the language L∞,ω1. Leo Harrington asked if one could improve this to the logic L∞, In [S. Shelah, Characterizing an -saturated model of superstable NDOP theories by its L∞,-theory, Israel Journal of Mathematics 140 61–111] Shelah gives a partial positive answer, showing that for T a countable superstable NDOP (...)
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  26.  2
    Nijmegen, The Netherlands July 27–August 2, 2006.Rodney Downey, Ieke Moerdijk, Boban Velickovic, Samson Abramsky, Marat Arslanov, Harvey Friedman, Martin Goldstern, Ehud Hrushovski, Jochen Koenigsmann & Andy Lewis - 2007 - Bulletin of Symbolic Logic 13 (2).
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