14 found
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  1.  8
    Lovely Pairs of Models.Itay Ben-Yaacov, Anand Pillay & Evgueni Vassiliev - 2003 - Annals of Pure and Applied Logic 122 (1-3):235-261.
    We introduce the notion of a lovely pair of models of a simple theory T, generalizing Poizat's “belles paires” of models of a stable theory and the third author's “generic pairs” of models of an SU-rank 1 theory. We characterize when a saturated model of the theory TP of lovely pairs is a lovely pair , finding an analog of the nonfinite cover property for simple theories. We show that, under these hypotheses, TP is also simple, and we study forking (...)
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  2.  13
    Positive Model Theory and Compact Abstract Theories.Itay Ben-Yaacov - 2003 - Journal of Mathematical Logic 3 (01):85-118.
  3.  20
    Simplicity in Compact Abstract Theories.Itay Ben-Yaacov - 2003 - Journal of Mathematical Logic 3 (02):163-191.
  4.  17
    Uncountable Dense Categoricity in Cats.Itay Ben-Yaacov - 2005 - Journal of Symbolic Logic 70 (3):829 - 860.
    We prove that under reasonable assumptions, every cat (compact abstract theory) is metric, and develop some of the theory of metric cats. We generalise Morley's theorem: if a countable Hausdorff cat T has a unique complete model of density character Λ ≥ ω₁, then it has a unique complete model of density character Λ for every Λ ≥ ω₁.
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  5.  43
    Lovely Pairs of Models: The Non First Order Case.Itay Ben-Yaacov - 2004 - Journal of Symbolic Logic 69 (3):641-662.
    We prove that for every simple theory T (or even simple thick compact abstract theory) there is a (unique) compact abstract theory $T^\mathfrak{B}$ whose saturated models are the lovely pairs of T. Independence-theoretic results that were proved in [5] when $T^\mathfrak{B}$ is a first order theory are proved for the general case: in particular $T^\mathfrak{B}$ is simple and we characterise independence.
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  6.  8
    Constructing an Almost Hyperdefinable Group.Itay Ben-Yaacov, Ivan Tomašić & Frank O. Wagner - 2004 - Journal of Mathematical Logic 4 (02):181-212.
  7.  8
    On the Fine Structure of the Polygroup Blow-Up.Itay Ben-Yaacov - 2003 - Archive for Mathematical Logic 42 (7):649-663.
    We study in detail the blow-up procedure described in [BTW01]. We obtain a structure theorem for coreless polygroups as a double quotient space G//H, and a polygroup chunk theorem. Seeking to remove the arbitrary parameter needed for the blow-up, we find canonical Ø-invariant groupoids.
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  8.  35
    Compactness and Independence in Non First Order Frameworks.Itay Ben-Yaacov - 2005 - Bulletin of Symbolic Logic 11 (1):28-50.
    This communication deals with positive model theory, a non first order model theoretic setting which preserves compactness at the cost of giving up negation. Positive model theory deals transparently with hyperimaginaries, and accommodates various analytic structures which defy direct first order treatment. We describe the development of simplicity theory in this setting, and an application to the lovely pairs of models of simple theories without the weak non finite cover property.
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  9.  34
    Discouraging Results for Ultraimaginary Independence Theory.Itay Ben-Yaacov - 2003 - Journal of Symbolic Logic 68 (3):846-850.
    Dividing independence for ultraimaginaries is neither symmetric nor transitive. Moreover, any notion of independence satisfying certain axioms (weaker than those for independence in a simple theory) and defined for all ultraimaginary sorts, is necessarily trivial.
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  10.  17
    Imaginaries in Hilbert Spaces.Itay Ben-Yaacov & Alexander Berenstein - 2003 - Archive for Mathematical Logic 43 (4):459-466.
    We characterise imaginaries (up to interdefinability) in Hilbert spaces using a Galois theory for compact unitary groups.
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  11.  19
    The Group Configuration in Simple Theories and its Applications.Itay Ben-Yaacov, Ivan Tomasic & Frank O. Wagner - 2002 - Bulletin of Symbolic Logic 8 (2):283-298.
    In recent work, the authors have established the group configuration theorem for simple theories, as well as some of its main applications from geometric stability theory, such as the binding group theorem, or in the $\omega$-categorical case, the characterization of the forking geometry of a finitely based non-trivial locally modular regular type as projective geometry over a finite field and the equivalence of pseudolinearity and local modularity. The proof necessitated an extension of the model-theoretic framework to include almost hyperimaginaries, and (...)
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  12.  2
    On Supersimplicity and Lovely Pairs of Cats.Itay Ben-Yaacov - 2006 - Journal of Symbolic Logic 71 (3):763 - 776.
    We prove that the definition of supersimplicity in metric structures from [7] is equivalent to an a priori stronger variant. This stronger variant is then used to prove that if T is a supersimple Hausdorff cat then so is its theory of lovely pairs.
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  13.  19
    Group Configurations and Germs in Simple Theories.Itay Ben-Yaacov - 2002 - Journal of Symbolic Logic 67 (4):1581-1600.
    We develop the theory of germs of generic functions in simple theories. Starting with an algebraic quadrangle (or other similar hypotheses), we obtain an "almost" generic group chunk, where the product is denned up to a bounded number of possible values. This is the first step towards the proof of the group configuration theorem for simple theories, which is completed in [3].
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  14.  5
    On Almost Orthogonality in Simple Theories.Itay Ben-Yaacov & Frank O. Wagner - 2004 - Journal of Symbolic Logic 69 (2):398 - 408.
    1. We show that if p is a real type which is internal in a set $\sigma$ of partial types in a simple theory, then there is a type p' interbounded with p, which is finitely generated over $\sigma$ , and possesses a fundamental system of solutions relative to $\sigma$ . 2. If p is a possibly hyperimaginary Lascar strong type, almost \sigma-internal$ , but almost orthogonal to $\sigma^{\omega}$ , then there is a canonical non-trivial almost hyperdefinable polygroup which multi-acts (...)
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