15 found
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  1.  39
    Forking and Dividing in NTP₂ Theories.Artem Chernikov & Itay Kaplan - 2012 - Journal of Symbolic Logic 77 (1):1-20.
    We prove that in theories without the tree property of the second kind (which include dependent and simple theories) forking and dividing over models are the same, and in fact over any extension base. As an application we show that dependence is equivalent to bounded non-forking assuming NTP 2.
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  2. Boolean Types in Dependent Theories.Itay Kaplan, Ori Segel & Saharon Shelah - forthcoming - Journal of Symbolic Logic:1-32.
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  3.  5
    Non-Forking and Preservation of NIP and Dp-Rank.Pedro Andrés Estevan & Itay Kaplan - 2021 - Annals of Pure and Applied Logic 172 (6):102946.
  4.  2
    Witnessing Dp-Rank.Itay Kaplan & Pierre Simon - 2014 - Notre Dame Journal of Formal Logic 55 (3):419-429.
    We prove that in $\operatorname {NTP}_{\operatorname {2}}$ theories the dp-rank of a type can be witnessed by indiscernible sequences of tuples satisfying that type. If the type has dp-rank infinity, then this can be witnessed by singletons.
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  5.  12
    An Embedding Theorem Of.Itay Kaplan & Benjamin D. Miller - 2014 - Journal of Mathematical Logic 14 (2):1450010.
    We provide a new criterion for embedding.
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  6.  5
    Exact Saturation in Simple and NIP Theories.Itay Kaplan, Saharon Shelah & Pierre Simon - 2017 - Journal of Mathematical Logic 17 (1):1750001.
    A theory [Formula: see text] is said to have exact saturation at a singular cardinal [Formula: see text] if it has a [Formula: see text]-saturated model which is not [Formula: see text]-saturated. We show, under some set-theoretic assumptions, that any simple theory has exact saturation. Also, an NIP theory has exact saturation if and only if it is not distal. This gives a new characterization of distality.
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  7.  10
    Examples in Dependent Theories.Itay Kaplan & Saharon Shelah - 2014 - Journal of Symbolic Logic 79 (2):585-619.
  8.  5
    Forcing a Countable Structure to Belong to the Ground Model.Itay Kaplan & Saharon Shelah - 2016 - Mathematical Logic Quarterly 62 (6):530-546.
    No categories
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  9.  7
    Criteria for Exact Saturation and Singular Compactness.Itay Kaplan, Nicholas Ramsey & Saharon Shelah - 2021 - Annals of Pure and Applied Logic 172 (9):102992.
    We introduce the class of unshreddable theories, which contains the simple and NIP theories, and prove that such theories have exactly saturated models in singular cardinals, satisfying certain set-theoretic hypotheses. We also give criteria for a theory to have singular compactness.
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  10.  8
    Chain Conditions in Dependent Groups.Itay Kaplan & Saharon Shelah - 2013 - Annals of Pure and Applied Logic 164 (12):1322-1337.
    In this note we prove and disprove some chain conditions in type definable and definable groups in dependent, strongly dependent and strongly2 dependent theories.
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  11.  12
    Strict Independence.Itay Kaplan & Alexander Usvyatsov - 2014 - Journal of Mathematical Logic 14 (2):1450008.
    We investigate the notions of strict independence and strict non-forking, and establish basic properties and connections between the two. In particular, it follows from our investigation that in resilient theories strict non-forking is symmetric. Based on this study, we develop notions of weight which characterize NTP2, dependence and strong dependence. Many of our proofs rely on careful analysis of sequences that witness dividing. We prove simple characterizations of such sequences in resilient theories, as well as of Morley sequences which are (...)
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  12.  10
    The Automorphism Tower of a Centerless Group Without Choice.Itay Kaplan & Saharon Shelah - 2009 - Archive for Mathematical Logic 48 (8):799-815.
    For a centerless group G, we can define its automorphism tower. We define G α : G 0 = G, G α+1 = Aut(G α ) and for limit ordinals ${G^{\delta}=\bigcup_{\alpha<\delta}G^{\alpha}}$ . Let τ G be the ordinal when the sequence stabilizes. Thomas’ celebrated theorem says ${\tau_{G}<(2^{|G|})^{+}}$ and more. If we consider Thomas’ proof too set theoretical (using Fodor’s lemma), we have here a more direct proof with little set theory. However, set theoretically we get a parallel theorem without the (...)
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  13.  1
    On Uniform Definability of Types Over Finite Sets for NIP Formulas.Shlomo Eshel & Itay Kaplan - 2020 - Journal of Mathematical Logic 21 (3).
    Combining two results from machine learning theory we prove that a formula is NIP if and only if it satisfies uniform definability of types over finite sets. This settles a conjecture of La...
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  14.  1
    On Uniform Definability of Types Over Finite Sets for NIP Formulas.Shlomo Eshel & Itay Kaplan - 2020 - Journal of Mathematical Logic 21 (3):2150015.
    Combining two results from machine learning theory we prove that a formula is NIP if and only if it satisfies uniform definability of types over finite sets. This settles a conjecture of La...
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  15.  2
    On the Automorphism Group of the Universal Homogeneous Meet-Tree.Itay Kaplan, Tomasz Rzepecki & Daoud Siniora - 2021 - Journal of Symbolic Logic 86 (4):1508-1540.
    We show that the countable universal homogeneous meet-tree has a generic automorphism, but does not have a generic pair of automorphisms.
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