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Arthur Apter (2003)
Some remarks on indestructibility and Hamkins’ lottery preparationArchive for Mathematical Logic, 42
J. Hamkins (1998)
Gap forcingIsrael Journal of Mathematics, 125
J. Hamkins (1998)
The Lottery PreparationAnn. Pure Appl. Log., 101
Arthur Apter, M. Gitik (1998)
The least measurable can be strongly compact and indestructibleJournal of Symbolic Logic, 63
Arthur Apter, J. Hamkins (2003)
Exactly controlling the non-supercompact strongly compact cardinalsJournal of Symbolic Logic, 68
Arthur Apter, J. Hamkins (1998)
Universal Indestructibility
M. Foreman (2020)
More saturated idealsLarge Cardinals, Determinacy and Other Topics
Arthur Apter (2005)
Universal Indestructibility is Consistent with Two Strongly Compact CardinalsBulletin of The Polish Academy of Sciences Mathematics, 53
J. Hamkins (1999)
Gap Forcing: Generalizing the Lévy-Solovay TheoremBulletin of Symbolic Logic, 5
Azriel Levy, R. Solovay (1967)
Measurable cardinals and the continuum hypothesisIsrael Journal of Mathematics, 5
Arthur Apter (2002)
Aspects of strong compactness, measurability, and indestructibilityArchive for Mathematical Logic, 41
Arthur Apter, G. Sargsyan (2006)
Identity crises and strong compactness III: Woodin cardinalsArchive for Mathematical Logic, 45
R. Laver (1978)
Making the supercompactness of κ indestructible under κ-directed closed forcingIsrael Journal of Mathematics, 29
J. Cummings (1992)
A model in which GCH holds at successors but fails at limitsTransactions of the American Mathematical Society, 329
We establish two theorems concerning strongly compact cardinals and universal indestructibility for degrees of supercompactness. In the first theorem, we show that universal indestructibility for degrees of supercompactness in the presence of a strongly compact cardinal is consistent with the existence of a proper class of measurable cardinals. In the second theorem, we show that universal indestructibility for degrees of supercompactness is consistent in the presence of two non-supercompact strongly compact cardinals, each of which exhibits a significant amount of indestructibility for its strong compactness.
Archive for Mathematical Logic – Springer Journals
Published: May 31, 2008
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