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  1.  36
    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.  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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  3.  9
    Examples in Dependent Theories.Itay Kaplan & Saharon Shelah - 2014 - Journal of Symbolic Logic 79 (2):585-619.
  4.  4
    An Embedding Theorem Of.Itay Kaplan & Benjamin D. Miller - 2014 - Journal of Mathematical Logic 14 (2):1450010.
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  5.  4
    Forcing a Countable Structure to Belong to the Ground Model.Itay Kaplan & Saharon Shelah - 2016 - Mathematical Logic Quarterly 62 (6):530-546.
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  6.  6
    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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  7.  12
    Strict Independence.Itay Kaplan & Alexander Usvyatsov - 2014 - Journal of Mathematical Logic 14 (2):1450008.
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  8.  5
    Exact Saturation in Simple and NIP Theories.Itay Kaplan, Saharon Shelah & Pierre Simon - 2017 - Journal of Mathematical Logic 17 (1):1750001.
    A theory T is said to have exact saturation at a singular cardinal κ if it has a κ-saturated model which is not κ+-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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  9.  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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