Results 1 to 10 of about 1,334 (95)
A note on δ-strongly compact cardinals
Topology and Its Applications, 2021 In this paper we investigate more characterizations and applications of $δ$-strongly compact cardinals. We show that, for a cardinal $κ$ the following are equivalent: (1) $κ$ is $δ$-strongly compact, (2) For every regular $λ\ge κ$ there is a $δ$-complete uniform ultrafilter over $λ$, and (3) Every product space of $δ$-Lindelöf spaces is $κ$-Lindelöf ...
Toshimichi Usuba
exaly +4 more sources
How large is the first strongly compact cardinal? or a study on identity crises
Annals of Mathematical Logic, 1976 AbstractIt is proved that if strongly compact cardinals are consistent, then it is consistent that the first such cardinal is the first measurable. On the other hand, if it is consistent to assume the existence of supercompact cardinal, then it is consistent to assume that it is the first strongly compact cardinal.
Menachem Magidor
exaly +2 more sources
ON THE COFINALITY OF THE LEAST $\lambda $ -STRONGLY COMPACT CARDINAL [PDF]
The Journal of Symbolic Logic, 2023 AbstractIn this paper, we characterize the possible cofinalities of the least $\lambda $ -strongly compact cardinal. We show that, on the one hand, for any regular cardinal, $\delta $ , that carries a $\lambda $ -complete uniform ultrafilter, it is consistent, relative to the existence of a supercompact cardinal above $\delta $ , that the least ...
Zhixing You, Jiachen Yuan
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Strongly compact cardinals and the continuum function [PDF]
Annals of Pure and Applied Logic, 2021 We study the general problem of the behaviour of the continuum function in the presence of non-supercompact strongly compact cardinals.
Arthur W. Apter +2 more
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ω1-strongly compact cardinals and normality
Topology and its Applications, 2023 We present more applications of the recently introduced -strongly compact cardinals in the context of either consistency or reflection results in General Topology, focusing on issues related to normality. In particular, we show that such large cardinal notion provides a new upper bound for the consistency strength of the statement “All normal Moore ...
Bagaria, Joan, da Silva, Samuel G.
openaire +2 more sources
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
doaj +1 more source
Exactly controlling the non-supercompact strongly compact cardinals [PDF]
Journal of Symbolic Logic, 2003 AbstractWe summarize the known methods of producing a non-supercompact strongly compact cardinal and describe some new variants. Our Main Theorem shows how to apply these methods to many cardinals simultaneously and exactly control which cardinals are supercompact and which are only strongly compact in a forcing extension.
Arthur W. Apter, Joel David Hamkins
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Strongly compact cardinals and ordinal definability
Journal of Mathematical Logic, 2023 This paper explores several topics related to Woodin’s HOD conjecture. We improve the large cardinal hypothesis of Woodin’s HOD dichotomy theorem from an extendible cardinal to a strongly compact cardinal. We show that assuming there is a strongly compact cardinal and the HOD hypothesis holds, there is no elementary embedding from HOD to HOD, settling
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On the first 𝑛 strongly compact cardinals [PDF]
Proceedings of the American Mathematical Society, 1995 Using techniques of Kimchi and Magidor, we generalize an earlier result and show that it is relatively consistent for the first n strongly compact cardinals to be somewhat supercompact yet not fully supercompact.
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Some results on [$n, m$]-paracompact and [$n, m$]-compact spaces
International Journal of Mathematics and Mathematical Sciences, 1997 Let n and m be infinite cardinals with n≤m and n be a regular cardinal. We prove certain implications of [n,m]-strongly paracompact, [n,m]-paracompact and [n,m]-metacompact spaces. Let X be [n,∞]-compact and Y be a [n,m]-paracompact (resp.
Hasan Z. Hdeib, Yusuf Ünlü
doaj +1 more source