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The Bulletin of Symbolic LogicAbstract This thesis presents my contributions to various aspects of the theory of universally Baire sets. One of these aspects is the smallest inner model containing all reals whose all sets of reals are universally Baire (viz.,
Obrad Kasum
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On $\omega $ -Strongly Measurable Cardinals
Forum of Mathematics, Sigma, 2023 We prove several consistency results concerning the notion of $\omega $ -strongly measurable cardinal in $\operatorname {\mathrm {HOD}}$ .
Omer Ben-Neria, Yair Hayut
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Forum of Mathematics, Sigma, 2023 Given an uncountable cardinal $\kappa $ , we consider the question of whether subsets of the power set of $\kappa $ that are usually constructed with the help of the axiom of choice are definable by $\Sigma _1$ -formulas that only use ...
Philipp Lücke, Sandra Müller
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Simultaneously vanishing higher derived limits
Forum of Mathematics, Pi, 2021 In 1988, Sibe Mardešić and Andrei Prasolov isolated an inverse system $\textbf {A}$ with the property that the additivity of strong homology on any class of spaces which includes the closed subsets of Euclidean space would entail that $\lim ^
Jeffrey Bergfalk, Chris Lambie-Hanson
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Hanf numbers via accessible images [PDF]
Logical Methods in Computer Science, 2017 We present several new model-theoretic applications of the fact that, under the assumption that there exists a proper class of almost strongly compact cardinals, the powerful image of any accessible functor is accessible.
Michael Lieberman, Jiri Rosicky
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Proof of a conjecture of Galvin
Forum of Mathematics, Pi, 2020 We prove that if the set of unordered pairs of real numbers is coloured by finitely many colours, there is a set of reals homeomorphic to the rationals whose pairs have at most two colours.
Dilip Raghavan, Stevo Todorcevic
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The new operations on complete ideals
Open Mathematics, 2019 We introduce the notion of K-ideals associated with Kuratowski partitions. Using new operations on complete ideals we show connections between K-ideals and precipitous ideals and prove that every complete ideal can be represented by some K-ideal.
Jureczko Joanna
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Forum of Mathematics, SigmaWe prove two compactness theorems for HOD. First, if $\kappa $ is a strong limit singular cardinal with uncountable cofinality and for stationarily many $\delta
Gabriel Goldberg, Alejandro Poveda
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Applications of the Magidor iteration to ultrafilter theory
Forum of Mathematics, SigmaWe characterize sums of normal ultrafilters after the Magidor iteration of Prikry forcings over a discrete set of measurable cardinals. We apply this to show that the weak Ultrapower Axiom is not equivalent to the Ultrapower Axiom.
Tom Benhamou, Gabriel Goldberg
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$\textsf {AD}^{+}$ implies $ \omega _{1}$ is a club $ \Theta $ -Berkeley cardinal
Forum of Mathematics, SigmaFollowing [1], given cardinals $\kappa
Douglas Blue, Grigor Sargsyan
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