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Creators/Authors contains: "Benhamou, Tom"

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  1. ; (, Journal of the London Mathematical Society)
    Abstract We demonstrate that the technology of Radin forcing can be used to transfer compactness properties at a weakly inaccessible but not strong limit cardinal to a strongly inaccessible cardinal. As an application, relative to the existence of large cardinals, we construct a model of set theory in which there is a strongly inaccessible cardinal that is ‐‐stationary for all but not weakly compact. This is in sharp contrast to the situation in the constructible universe , where being ‐‐stationary is equivalent to being ‐indescribable. We also show that it is consistent that there is a cardinal such that is ‐stationary for all and , answering a question of Sakai. 
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  2. ; (, Canadian Journal of Mathematics)
    Abstract We continue the study of the Galvin property from Benhamou, Garti, and Shelah (2023,Proceedings of the American Mathematical Society151, 1301–1309) and Benhamou (2023,Saturation properties in canonical inner models, submitted). In particular, we deepen the connection between certain diamond-like principles and non-Galvin ultrafilters. We also show that any Dodd sound nonp-point ultrafilter is non-Galvin. We use these ideas to formulate what appears to be the optimal large cardinal hypothesis implying the existence of a non-Galvin ultrafilter, improving on a result from Benhamou and Dobrinen (2023,Journal of Symbolic Logic, 1–34). Finally, we use a strengthening of the Ultrapower Axiom to prove that in all the known canonical inner models, a$$\kappa $$-complete ultrafilter has the Galvin property if and only if it is an iterated sum ofp-points. 
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  3. ; (, The Journal of Symbolic Logic)
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  4. ; ; ; (, Journal of Mathematical Logic)
    We address the question of consistency strength of certain filters and ultrafilters which fail to satisfy the Galvin property. We answer questions [Benhamou and Gitik, Ann. Pure Appl. Logic 173 (2022) 103107; Questions 7.8, 7.9], [Benhamou et al., J. Lond. Math. Soc. 108(1) (2023) 190–237; Question 5] and improve theorem [Benhamou et al., J. Lond. Math. Soc. 108(1) (2023) 190–237; Theorem 2.3]. 
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