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20Generic expansion and Skolemization in NSOP 1 theoriesAnnals of Pure and Applied Logic 169 (8): 755-774. 2018.
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19On model-theoretic tree propertiesJournal of Mathematical Logic 16 (2): 1650009. 2016.We study model theoretic tree properties and their associated cardinal invariants. In particular, we obtain a quantitative refinement of Shelah’s theorem for countable theories, show that [Formula: see text] is always witnessed by a formula in a single variable and that weak [Formula: see text] is equivalent to [Formula: see text]. Besides, we give a characterization of [Formula: see text] via a version of independent amalgamation of types and apply this criterion to verify that some examples in…Read more
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18Brain Activity Associated With Expected Task DifficultyFrontiers in Human Neuroscience 13. 2019.
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14Transitivity, Lowness, and Ranks in Nsop TheoriesJournal of Symbolic Logic 88 (3): 919-946. 2023.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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13Independence over arbitrary sets in NSOP1 theoriesAnnals of Pure and Applied Logic 173 (2): 103058. 2022.We study Kim-independence over arbitrary sets. Assuming that forking satisfies existence, we establish Kim's lemma for Kim-dividing over arbitrary sets in an NSOP1 theory. We deduce symmetry of Kim-independence and the independence theorem for Lascar strong types
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12Criteria for exact saturation and singular compactnessAnnals of Pure and Applied Logic 172 (9): 102992. 2021.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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10Exact saturation in pseudo-elementary classes for simple and stable theoriesJournal of Mathematical Logic 23 (2). 2022.We use exact saturation to study the complexity of unstable theories, showing that a variant of this notion called pseudo-elementary class (PC)-exact saturation meaningfully reflects combinatorial dividing lines. We study PC-exact saturation for stable and simple theories. Among other results, we show that PC-exact saturation characterizes the stability cardinals of size at least continuum of a countable stable theory and, additionally, that simple unstable theories have PC-exact saturation at s…Read more
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10Invariant measures in simple and in small theoriesJournal of Mathematical Logic 23 (2). 2023.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 discret…Read more
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University of California, Los AngelesPost-doctoral Fellow
Los Angeles, California, United States of America