Results for 'Ita�� Ben Yaacov'

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  1.  42
    Topometric Spaces and Perturbations of Metric Structures.Itaï Ben Yaacov - 2008 - Logic and Analysis 1 (3-4):235-272.
    We develop the general theory of topometric spaces, i.e., topological spaces equipped with a well-behaved lower semi-continuous metric. Spaces of global and local types in continuous logic are the motivating examples for the study of such spaces. In particular, we develop Cantor-Bendixson analysis of topometric spaces, which can serve as a basis for the study of local stability (extending the ad hoc development in Ben Yaacov I and Usvyatsov A, Continuous first order logic and local stability. Trans Am Math (...)
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  2.  27
    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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  3.  32
    Fondements de la Logique Positive.Ben Yaacov Itaï & Poizat Bruno - 2007 - Journal of Symbolic Logic 72 (4):1141-1162.
    We revisit the foundations of positive model theory, introducing h-inductive sentences. These allow a considerably simplified presentation of positive model theory, as well as a characterisation of Hausdorff cats by an amalgamation property of their h-inductive theory.
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  4.  61
    Positive Model Theory and Compact Abstract Theories.Itay Ben-Yaacov - 2003 - Journal of Mathematical Logic 3 (01):85-118.
    We develop positive model theory, which is a non first order analogue of classical model theory where compactness is kept at the expense of negation. The analogue of a first order theory in this framework is a compact abstract theory: several equivalent yet conceptually different presentations of this notion are given. We prove in particular that Banach and Hilbert spaces are compact abstract theories, and in fact very well-behaved as such.
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  5.  43
    Simplicity in Compact Abstract Theories.Itay Ben-Yaacov - 2003 - Journal of Mathematical Logic 3 (02):163-191.
    We continue [2], developing simplicity in the framework of compact abstract theories. Due to the generality of the context we need to introduce definitions which differ somewhat from the ones use in first order theories. With these modified tools we obtain more or less classical behaviour: simplicity is characterized by the existence of a certain notion of independence, stability is characterized by simplicity and bounded multiplicity, and hyperimaginary canonical bases exist.
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  6.  13
    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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  7.  10
    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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  8.  13
    Model Theoretic Forcing in Analysis.Itaï Ben Yaacov & José Iovino - 2009 - Annals of Pure and Applied Logic 158 (3):163-174.
    We present a framework for model theoretic forcing in a non first order context, and present some applications of this framework to Banach space theory.
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  9.  34
    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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  10.  13
    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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  11.  13
    Constructing an Almost Hyperdefinable Group.Itay Ben-Yaacov, Ivan Tomašić & Frank O. Wagner - 2004 - Journal of Mathematical Logic 4 (02):181-212.
    This paper completes the proof of the group configuration theorem for simple theories started in [1]. We introduce the notion of an almost hyperdefinable structure, and show that it has a reasonable model theory. We then construct an almost hyperdefinable group from a polygroup chunk.
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  12.  7
    Definability of Groups in ℵ₀-Stable Metric Structures.Itaï Ben Yaacov - 2010 - Journal of Symbolic Logic 75 (3):817-840.
    We prove that in a continuous ℵ₀-stable theory every type-definable group is definable. The two main ingredients in the proof are: 1. Results concerning Morley ranks (i.e., Cantor-Bendixson ranks) from [Ben08], allowing us to prove the theorem in case the metric is invariant under the group action; and 2. Results concerning the existence of translation-invariant definable metrics on type-definable groups and the extension of partial definable metrics to total ones.
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  13.  99
    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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  14.  24
    The Group Configuration in Simple Theories and its Applications.Itay Ben-Yaacov, Ivan Tomašić & 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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  15.  9
    Grey Subsets of Polish Spaces.Itaï Ben Yaacov & Julien Melleray - 2015 - Journal of Symbolic Logic 80 (4):1379-1397.
  16.  51
    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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  17.  27
    Imaginaries in Hilbert Spaces.Itay Ben-Yaacov & Alexander Berenstein - 2004 - 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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  18.  35
    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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  19. Ben-Yaacov, I., Pillay, A. And Vassiliev, E., Lovely Pairs Of.A. Khelif, S. Neumann & Z. Petric - 2003 - Annals of Pure and Applied Logic 122:293.
  20. Foundations of Positive Logic.Itai Ben Yaacov & Bruno Poizat - 2007 - Journal of Symbolic Logic 72 (4):1141-1162.
  21.  9
    Reconstruction of Separably Categorical Metric Structures.Itaï Ben Yaacov & Adriane Kaïchouh - 2016 - Journal of Symbolic Logic 81 (1):216-224.
  22.  6
    Simple Almost Hyperdefinable Groups.Itaï Ben-Yaacov - 2006 - Journal of Mathematical Logic 6 (01):69-88.
    We lay down the groundwork for the treatment of almost hyperdefinable groups: notions from [5] are put into a natural hierarchy, and new notions, essential to the study to such groups, fit elegantly into this hierarchy. We show that "classical" properties of definable and hyperdefinable groups in simple theories can be generalised to this context. In particular, we prove the existence of stabilisers of Lascar strong types and of the connected and locally connected components of subgroups, and that in a (...)
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  23.  19
    On Perturbations of Continuous Structures.Itaï Ben Yaacov - 2008 - Journal of Mathematical Logic 8 (2):225-249.
    We give a general framework for the treatment of perturbations of types and structures in continuous logic, allowing to specify which parts of the logic may be perturbed. We prove that separable, elementarily equivalent structures which are approximately $aleph_0$-saturated up to arbitrarily small perturbations are isomorphic up to arbitrarily small perturbations. As a corollary, we obtain a Ryll-Nardzewski style characterisation of complete theories all of whose separable models are isomorphic up to arbitrarily small perturbations.
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  24.  12
    An Independence Theorem for Ntp2 Theories.Itaï Ben Yaacov & Artem Chernikov - 2014 - Journal of Symbolic Logic 79 (1):135-153.
  25.  39
    Continuous First Order Logic for Unbounded Metric Structures.Itaï Ben Yaacov - 2008 - Journal of Mathematical Logic 8 (2):197-223.
    We present an adaptation of continuous first order logic to unbounded metric structures. This has the advantage of being closer in spirit to C. Ward Henson's logic for Banach space structures than the unit ball approach, as well as of applying in situations where the unit ball approach does not apply. We also introduce the process of single point emph{emboundment}, allowing to bring unbounded structures back into the setting of bounded continuous first order logic. Together with results from cite{BenYaacov:Perturbations} regarding (...)
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  26.  46
    A Proof of Completeness for Continuous First-Order Logic.Itaï Ben Yaacov & Arthur Paul Pedersen - 2010 - Journal of Symbolic Logic 75 (1):168-190.
    -/- Continuous first-order logic has found interest among model theorists who wish to extend the classical analysis of “algebraic” structures (such as fields, group, and graphs) to various natural classes of complete metric structures (such as probability algebras, Hilbert spaces, and Banach spaces). With research in continuous first-order logic preoccupied with studying the model theory of this framework, we find a natural question calls for attention. Is there an interesting set of axioms yielding a completeness result? -/- The primary purpose (...)
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  27.  19
    Fondements de la Logique Positive.Itaï Ben Yaacov & Et Bruno Poizat - 2007 - Journal of Symbolic Logic 72 (4):1141-1162.
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  28. Lovely Pairs of Models: The Non First Order Case.Itaï 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 $T^fP$ whose saturated models are the lovely pairs of $T$. Independence-theoretic results that were proved in [Ben Yaacov, Pillay, Vassiliev - Lovely pairs of models] when $T^fP$ is a first order theory are proved for the general case: in particular $T^fP$ is simple and we characterise independence.
     
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  29. On Supersimplicity and Lovely Pairs of Cats.Itaï Ben Yaacov - 2006 - Journal of Symbolic Logic 71 (3):763-776.
    We prove that the definition of supersimplicity in metric structures from [Ben Yaacov, Uncountable dense categoricity in cats] is equivalent to an textit{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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  30.  11
    Model Theoretic Stability and Definability of Types, After A. Grothendieck.Itaï Ben Yaacov - 2014 - Bulletin of Symbolic Logic 20 (4):491-496,.
    We point out how the "Fundamental Theorem of Stability Theory", namely the equivalence between the "non order property" and definability of types, proved by Shelah in the 1970s, is in fact an immediate consequence of Grothendieck's "Criteres de compacite" from 1952. The familiar forms for the defining formulae then follow using Mazur's Lemma regarding weak convergence in Banach spaces.
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  31.  31
    A Proof Of Completeness For Continuous First-Order Logic.Arthur Pedersen & Itaï Ben Yaacov - 2010 - Journal of Symbolic Logic 75 (1):168-190.
    Continuous first-order logic has found interest among model theorists who wish to extend the classical analysis of “algebraic” structures to various natural classes of complete metric structures. With research in continuous first-order logic preoccupied with studying the model theory of this framework, we find a natural question calls for attention. Is there an interesting set of axioms yielding a completeness result?The primary purpose of this article is to show that a certain, interesting set of axioms does indeed yield a completeness (...)
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  32.  11
    Stability and Stable Groups in Continuous Logic.Itaï Ben Yaacov - 2010 - Journal of Symbolic Logic 75 (3):1111-1136.
    We develop several aspects of local and global stability in continuous first order logic. In particular, we study type-definable groups and genericity.
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  33.  20
    Law and Internal Cultural Conflicts.Yaacov Ben-Shemesh - 2007 - Law and Ethics of Human Rights 1 (1):271-308.
    Liberal political theory acknowledges the interdependence of the wellbeing of individuals and the flourishing of the cultural groups to which they belong. Consequently, many liberal political philosophers have proposed policies and laws aimed at multicultural accommodation. That is, policies and laws aimed at assisting communities to preserve their cultural values and practices, and at allowing them greater autonomy and self-government. However, certain religious and cultural groups hold beliefs, values, and practices that are oppressive and discriminatory against some of their own (...)
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  34.  7
    Almost Indiscernible Sequences and Convergence of Canonical Bases.Itaï Ben Yaacov, Alexander Berenstein & C. Ward Henson - 2014 - Journal of Symbolic Logic 79 (2):460-484.
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  35.  2
    A Metric Version of Schlichting’s Theorem.Itaï Ben Yaacov & Frank O. Wagner - 2020 - Journal of Symbolic Logic 85 (4):1607-1613.
    If ${\mathfrak {F}}$ is a type-definable family of commensurable subsets, subgroups or subvector spaces in a metric structure, then there is an invariant subset, subgroup or subvector space commensurable with ${\mathfrak {F}}$. This in particular applies to type-definable or hyper-definable objects in a classical first-order structure.
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  36.  3
    Fraïssé Limits of Metric Structures.Itaï Ben Yaacov - 2015 - Journal of Symbolic Logic 80 (1):100-115.
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  37.  33
    Ilijas Farah, Bradd Hart, and David Sherman. Model Theory of Operator Algebras I: Stability. Bulletin of the London Mathematical Society, Vol. 45 , No. 4, Pp. 825–838, Doi:10.1112/Blms/Bdt014. - Ilijas Farah, Bradd Hart, and David Sherman. Model Theory of Operator Algebras II: Model Theory. Israel Journal of Mathematics, Vol. 201 , No. 1, Pp. 477–505, Doi:10.1007/S11856-014-1046-7. - Ilijas Farah, Bradd Hart, and David Sherman. Model Theory of Operator Algebras III: Elementary Equivalence and II1factors. Bulletin of the London Mathematical Society, Vol. 46 , No. 3, Pp. 609–628, Doi:10.1112/Blms/Bdu012. - Isaac Goldbring, Bradd Hart, and Thomas Sinclair. The Theory of Tracial von Neumann Algebras Does Not Have a Model Companion. Journal of Symbolic Logic, Vol. 78 , No. 3, Pp. 1000–1004. [REVIEW]Itaï Ben Yaacov - 2015 - Bulletin of Symbolic Logic 21 (4):425-427.
  38.  4
    Model Theoretic Properties of Metric Valued Fields.Itaï Ben Yaacov - 2014 - Journal of Symbolic Logic 79 (3):655-675.
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  39.  31
    Immigration Rights and the Demographic Consideration.Yaacov Ben-Shemesh - 2008 - Law and Ethics of Human Rights 2 (1):1-34.
    Attaining and maintaining a substantial Jewish majority in Israel has been one of the basic goals of the State of Israel since its early years. A substantial Jewish majority within the borders of the state is thought to be necessary in order to preserve its Jewish nature. Many believe that the demographic consideration also stood behind the enactment of the Citizenship and Entry into Israel Law , 2003, which prohibits granting Israeli citizenship and residency to Palestinians from the West Bank (...)
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  40. Knowledge and Religion in Early Modern Europe: Studies in Honor of Michael Heyd.Asaph Ben-Tov, Yaacov Deutsch & Tamar Herzig (eds.) - 2013 - Brill.
    This collection of essays examines interplays of knowledge and religion in early modern thought. Spanning from the sixteenth to the eighteenth century, it considers varied formations of knowledge and religion, knowledge about religion and irreligious knowledge in early modern Europe.
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  41.  26
    Neutrality Without Autonomy.Yaacov Ben-Shemesh - 2004 - Law and Philosophy 24 (5):435-466.
  42.  8
    Religion and the Democratic Tradition.Yaacov Ben-Shemesh - 2004 - Social Theory and Practice 30 (3):429-443.
  43.  8
    Omitting Types in Logic of Metric Structures.Ilijas Farah & Menachem Magidor - 2018 - Journal of Mathematical Logic 18 (2):1850006.
    This paper is about omitting types in logic of metric structures introduced by Ben Yaacov, Berenstein, Henson and Usvyatsov. While a complete type is omissible in some model of a countable complete...
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  44.  27
    Omitting Types for Infinitary[0,1]-Valued Logic.Christopher J. Eagle - 2014 - Annals of Pure and Applied Logic 165 (3):913-932.
    We describe an infinitary logic for metric structures which is analogous to Lω1,ω. We show that this logic is capable of expressing several concepts from analysis that cannot be expressed in finitary continuous logic. Using topological methods, we prove an omitting types theorem for countable fragments of our infinitary logic. We use omitting types to prove a two-cardinal theorem, which yields a strengthening of a result of Ben Yaacov and Iovino concerning separable quotients of Banach spaces.
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  45.  18
    Quelques Effets Pervers de la Positivité.Bruno Poizat - 2010 - Annals of Pure and Applied Logic 161 (6):812-816.
    La Logique positive a été introduite au début de ce troisième millénaire par Itaï Ben Yaacov, qui y a été conduit par une nécessité interne à la Théorie des modèles. Dans ce contexte de validité du Théorème de compacité, l’absence de négation provoque des situations inhabituelles, comme celle des structures infinies qui ont une extension élémentaire maximale, que nous étudions ici.
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  46.  3
    Reduction of Database Independence to Dividing in Atomless Boolean Algebras.Tapani Hyttinen & Gianluca Paolini - 2016 - Archive for Mathematical Logic 55 (3-4):505-518.
    We prove that the form of conditional independence at play in database theory and independence logic is reducible to the first-order dividing calculus in the theory of atomless Boolean algebras. This establishes interesting connections between independence in database theory and stochastic independence. As indeed, in light of the aforementioned reduction and recent work of Ben-Yaacov :957–1012, 2013), the former case of independence can be seen as the discrete version of the latter.
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  47.  13
    Positive Model Theory and Amalgamations.Mohammed Belkasmi - 2014 - Notre Dame Journal of Formal Logic 55 (2):205-230.
    We continue the analysis of foundations of positive model theory as introduced by Ben Yaacov and Poizat. The objects of this analysis are $h$-inductive theories and their models, especially the “positively” existentially closed ones. We analyze topological properties of spaces of types, introduce forms of quantifier elimination, and characterize minimal completions of arbitrary $h$-inductive theories. The main technical tools consist of various forms of amalgamations in special classes of structures.
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  48.  1
    On Amalgamation in NTP $_{2}$ Theories and Generically Simple Generics.Pierre Simon - 2020 - Notre Dame Journal of Formal Logic 61 (2):233-243.
    We prove a couple of results on NTP2 theories. First, we prove an amalgamation statement and deduce from it that the Lascar distance over extension bases is bounded by 2. This improves previous work of Ben Yaacov and Chernikov. We propose a line of investigation of NTP2 theories based on S1 ideals with amalgamation and ask some questions. We then define and study a class of groups with generically simple generics, generalizing NIP groups with generically stable generics.
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  49.  11
    A Completeness Theorem for Continuous Predicate Modal Logic.Stefano Baratella - 2019 - Archive for Mathematical Logic 58 (1-2):183-201.
    We study a modal extension of the Continuous First-Order Logic of Ben Yaacov and Pedersen :168–190, 2010). We provide a set of axioms for such an extension. Deduction rules are just Modus Ponens and Necessitation. We prove that our system is sound with respect to a Kripke semantics and, building on Ben Yaacov and Pedersen, that it satisfies a number of properties similar to those of first-order predicate logic. Then, by means of a canonical model construction, we get (...)
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  50.  56
    Construal-Level Theory of Psychological Distance.Yaacov Trope & Nira Liberman - 2010 - Psychological Review 117 (2):440-463.
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