Results 31 to 40 of about 218 (121)
The two-cardinals transfer property and resurrection of supercompactness span style=color:red\textbf{This article has been retracted}/span [PDF]
Proceedings of the American Mathematical Society, 1996 span style=color:red\textbf{This article has been retracted.}/span We show that the transfer property ( ℵ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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On the cofinality of the least λ-strongly compact cardinal [PDF]
In this paper, we characterize the possible cofinalities of the least λ-strongly compact cardinal.We show that, on the one hand, for any regular cardinal, δ, that carries a λ-complete uniform ultrafilter, it is consistent, relative to the existence of a ...
You, Z +3 more
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The Wholeness Axioms and the Class of Supercompact Cardinals
Bulletin of the Polish Academy of Sciences Mathematics, 2012 We show that certain relatively consistent structural properties of the class of supercompact cardinals are also relatively consistent with the Wholeness Axioms.
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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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How large is the first strongly compact cardinal? or a study on identity crises
, 1976 It 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 ...
Magidor, Menachem
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A stationary-tower-free proof of sealing from a supercompact
, 2022 Sealing is a generic absoluteness principle for the theory of the universally Baire sets of reals introduced by Woodin. It is deeply connected to the Inner Model Program and plays a prominent role in recent advances in inner model theory.
Müller, Sandra; orcid:
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A Note on Indestructibility and Strong Compactness [PDF]
, 2008 If κ < λ are such that κ is both supercompact and indestructible under κ-directed closed forcing which is also (κ+,∞)-distributive and λ is 2λ supercompact, then by [3, Theorem 5], {δ < κ | δ is δ+ strongly compact yet δ isn’t δ+ supercompact} must
Arthur W. Apter
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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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, 1998 We construct a model in which there are no ℵn-Aronszajn trees for any finiten⩾2, starting from a model with infinitely many supercompact cardinals.
Foreman, Matthew, Cummings, James
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WEAK SQUARES AND VERY GOOD SCALES
, 2018 We assume the existence of a supercompact cardinal and produce a model with weak square but no very good scale at a particular cardinal. This follows work of Cummings, Foreman, and Magidor, but uses a different approach.
MAXWELL LEVINE
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