Results 1 to 10 of about 40 (40)
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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A model of the Axiom of Determinacy in which every set of reals is universally Baire
Forum of Mathematics, SigmaThe consistency of the theory $\mathsf {ZF} + \mathsf {AD}_{\mathbb {R}} + {}$ ‘every set of reals is universally Baire’ is proved relative to $\mathsf {ZFC} + {}$ ‘there is a cardinal that is a limit of Woodin cardinals and of strong ...
Paul B. Larson +2 more
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