Results 31 to 40 of about 199 (115)
CHANG’S CONJECTURE, GENERIC ELEMENTARY EMBEDDINGS AND INNER MODELS FOR HUGE CARDINALS [PDF]
, 2015 We introduce a natural principle Strong Chang Reflection strengthening the classical Chang Conjectures. This principle is between a huge and a two huge cardinal in consistency strength.
FOREMAN, MATTHEW
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, 1997 We show relative to strong hypotheses that patterns of compact cardinals in the universe, where a compact cardinal is one which is either strongly compact or supercompact, can be virtually arbitrary.
Apter, Arthur W.
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On the first 𝑛 strongly compact cardinals
, 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.
Arthur W. Apter
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The two-cardinals transfer property and resurrection of supercompactness span style=color:red\textbf{This article has been retracted}/span [PDF]
Proceedings of the American Mathematical Society, 1996 span style=color:red\textbf{This article has been retracted.}/span We show that the transfer property ( ℵ
Shai Ben-David, Saharon Shelah
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Mathematical Logic Quarterly, 2001 We show that if the weak compactness of a cardinal is made indestructible by means of any preparatory forcing of a certain general type, including any forcing naively resembling the Laver preparation, then the cardinal was originally supercompact. We then apply this theorem to show that the hypothesis of supercompactness is necessary for certain proof ...
Arthur W. Apter, Joel David Hamkins
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Definable tree property for uncountable regular cardinals
, 2023 The primary goal of this paper is to establish a model of $ZFC$ wherein the definable tree property is affirmed for all uncountable regular cardinals. This endeavor commences with the utilization of both a supercompact cardinal and a measurable cardinal ...
Golshani, Mohammad, Mirabi, Mostafa
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THE STRONG TREE PROPERTY AT SUCCESSORS OF SINGULAR CARDINALS
, 2014 International audienceAbstract An inaccessible cardinal is strongly compact if, and only if, it satisfies the strong tree property. We prove that if there is a model of ZFC with infinitely many supercompact cardinals, then there is a model of ZFC where ${
Fontanella, Laura
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A framework for forcing constructions at successors of singular cardinals
, 2018 We describe a framework for proving consistency results about singular cardinals of arbitrary cofinality and their successors. This framework allows the construction of models in which the Singular Cardinals Hypothesis fails at a singular cardinal κ of ...
Mirna Dzamonja (5364554) +4 more
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A framework for forcing constructions at successors of singular cardinals
, 2017 We describe a framework for proving consistency results about singular cardinals of arbitrary cofinality and their successors. This framework allows the construction of models in which the Singular Cardinals Hypothesis fails at a singular cardinal κ of ...
Dzamonja, Mirna +4 more
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Chang's conjecture may fail at supercompact cardinals
, 2006 We prove a revised version of Laver's indestructibility theorem which slightly improves over the classical result. An application yields the consistency of $(\kappa^+,\kappa)\notcc(\aleph_1,\aleph_0)$ when $\kappa$ is supercompact. The actual proofs show
Koenig, Bernhard
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