Results 211 to 220 of about 1,520 (239)
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More on the Least Strongly Compact Cardinal
Mathematical Logic Quarterly, 1997AbstractWe show that it is consistent, relative to a supercompact limit of supercompact cardinals, for the least strongly compact cardinal k to be both the least measurable cardinal and to be > 2k supercompact.
Arthur W Apter
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On the least strongly compact cardinal
Israel Journal of Mathematics, 1980We prove that under the assumption of a supercompact cardinal κ which is a limit of supercompact cardinals, for any increasing Σ2 function φ the set {∂
Arthur W Apter, Apter Arthur W
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Normal measures and strongly compact cardinals
Bolletino Dell Unione Matematica Italiana, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Arthur W Apter, Apter Arthur W
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Diamond (on the regulars) can fail at any strongly unfoldable cardinal
Annals of Pure and Applied Logic, 2006 If ? is any strongly unfoldable cardinal, then this is preserved in a forcing extension in which ??(REG) fails. This result continues the progression of the corresponding results for weakly compact cardinals, due to Woodin, and for indescribable ...
Mirna Džamonja, Joel David Hamkins
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ON ${\omega _1}$-STRONGLY COMPACT CARDINALS
The Journal of Symbolic Logic, 2014Abstract An uncountable cardinal κ is called ${\omega _1}$ -strongly compact if every κ-complete ultrafilter on any set I can be extended to an
Joan Bagaria, Menachem Magidor
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Tall, Strong, and Strongly Compact Cardinals
Sarajevo Journal of Mathematics, 2022We construct three models in which there are different relationships among the classes of strongly compact, strong, and non-strong tall cardinals. In the first two of these models, the strongly compact and strong cardinals coincide precisely, and every strongly compact/strong cardinal is a limit of non-strong tall cardinals. In the remaining model, the
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Strong compactness and the ultrapower axiom I: the least strongly compact cardinal
Journal of Mathematical Logic, 2022The Ultrapower Axiom is a combinatorial principle concerning the structure of large cardinals that is true in all known canonical inner models of set theory. A longstanding test question for inner model theory is the equiconsistency of strongly compact and supercompact cardinals.
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INDESTRUCTIBILITY WHEN THE FIRST TWO MEASURABLE CARDINALS ARE STRONGLY COMPACT
The Journal of Symbolic Logic, 2021AbstractWe prove two theorems concerning indestructibility properties of the first two strongly compact cardinals when these cardinals are in addition the first two measurable cardinals. Starting from two supercompact cardinals $\kappa _1 < \kappa _2$ , we force and construct a model in which $\kappa _1$ and $\kappa _2$ are both the first two ...
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G-covers, strongly compact cardinals and factorization of maps from products in Unif and Top
Topology and its Applications, 2023To a great extent, this paper builds upon the articles [\textit{M. Hušek}, Topology Appl. 304, Article ID 107792, 18 p. (2021; Zbl 1482.54032); \textit{M. Hušek} and \textit{J. Rosický}, ibid. 259, 251--266 (2019; Zbl 1417.54006)], emphasizing its focus on achieving better results. The article [\textit{M. Hušek}, ibid.
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Some results concerning strongly compact cardinals
Journal of Symbolic Logic, 1985This paper consists of two parts. In §1 we mention the first strongly compact cardinal. Magidor proved in [6] that it can be the first measurable and it can be also the first supercompact. In [2], Apter proved that Con(ZFC + there is a supercompact limit of supercompact cardinals) implies Con(ZFC + the first strongly compact cardinal κ is ϕ(κ ...
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