Archive for Mathematical Logic 47 (2):133-142 (2008)
| Abstract |
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
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| Keywords | Universal indestructibility Indestructibility Measurable cardinal Strongly compact cardinal Supercompact cardinal |
| Categories | (categorize this paper) |
| DOI | 10.1007/s00153-008-0072-8 |
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References found in this work BETA
The Lottery Preparation.Joel David Hamkins - 2000 - Annals of Pure and Applied Logic 101 (2-3):103-146.
Gap Forcing: Generalizing the Lévy-Solovay Theorem.Joel David Hamkins - 1999 - Bulletin of Symbolic Logic 5 (2):264-272.
The Least Measurable Can Be Strongly Compact and Indestructible.Arthur W. Apter & Moti Gitik - 1998 - Journal of Symbolic Logic 63 (4):1404-1412.
Exactly Controlling the Non-Supercompact Strongly Compact Cardinals.Arthur W. Apter & Joel David Hamkins - 2003 - Journal of Symbolic Logic 68 (2):669-688.
Identity Crises and Strong Compactness III: Woodin Cardinals. [REVIEW]Arthur W. Apter & Grigor Sargsyan - 2006 - Archive for Mathematical Logic 45 (3):307-322.
View all 8 references / Add more references
Citations of this work BETA
On the Indestructibility Aspects of Identity Crisis.Grigor Sargsyan - 2009 - Archive for Mathematical Logic 48 (6):493-513.
Indestructibility When the First Two Measurable Cardinals Are Strongly Compact.Arthur W. Apter - 2022 - Journal of Symbolic Logic 87 (1):214-227.
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