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  1. ; (, Proceedings of the 14th Panhellenic Logic Symposium)
    Kavvos, Alex; Gregoriades, Vassilis (Ed.)
    For n∈ℕ and ε>0, given a sufficiently long sequence of events in a probability space all of measure at least ε, some n of them will have a common intersection. A more subtle pattern: for any 0<1, we cannot find events Ai and Bi so that μ(Ai∩Bj)≤p and μ(Aj∩Bi)≥q for all 1 
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  2. ; ; (, Duke Mathematical Journal)
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  3. (, The Journal of Symbolic Logic)
    We provide polynomial upper bounds for the minimal sizes of distal cell decompositions in several kinds of distal structures, particularly weakly o-minimal and P-minimal structures. The bound in general weakly o-minimal structures generalizes the vertical cell decomposition for semialgebraic sets, and the bounds for vector spaces in both o-minimal and p-adic cases are tight. We apply these bounds to Zarankiewicz's problem and sum-product bounds in distal structures. 
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  4. ; ; ; ; ; ; (, Journal of Mathematical Logic)
    We give examples of (i) a simple theory with a formula (with parameters) which does not fork over [Formula: see text] but has [Formula: see text]-measure 0 for every automorphism invariant Keisler measure [Formula: see text] and (ii) a definable group [Formula: see text] in a simple theory such that [Formula: see text] is not definably amenable, i.e. there is no translation invariant Keisler measure on [Formula: see text]. We also discuss paradoxical decompositions both in the setting of discrete groups and of definable groups, and prove some positive results about small theories, including the definable amenability of definable groups. 
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  5. ; ; (, The Journal of Symbolic Logic)
    Abstract We develop the theory of Kim-independence in the context of NSOP $$_{1}$$ theories satisfying the existence axiom. We show that, in such theories, Kim-independence is transitive and that -Morley sequences witness Kim-dividing. As applications, we show that, under the assumption of existence, in a low NSOP $$_{1}$$ theory, Shelah strong types and Lascar strong types coincide and, additionally, we introduce a notion of rank for NSOP $$_{1}$$ theories. 
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  6. ; (, The Journal of Symbolic Logic)
    Abstract We introduce and study (weakly) semi-equational theories, generalizing equationality in stable theories (in the sense of Srour) to the NIP context. In particular, we establish a connection to distality via one-sided strong honest definitions; demonstrate that certain trees are semi-equational, while algebraically closed valued fields are not weakly semi-equational; and obtain a general criterion for weak semi-equationality of an expansion of a distal structure by a new predicate. 
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  7. ; (, Model Theory)
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  8. ; (, Pacific Journal of Mathematics)
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  9. ; ; (, Model Theory)
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  10. ; (, Israel Journal of Mathematics)
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