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Indestructible Weakly Compact Cardinals and the Necessity of Supercompactness for Certain Proof Schemata
Mathematical Logic Quarterly 47 (4):563-572 (2001)
Abstract
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 schemataAuthor's Profile
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Citations of this work
Indestructible Strong Unfoldability.Joel David Hamkins & Thomas A. Johnstone - 2010 - Notre Dame Journal of Formal Logic 51 (3):291-321.
The least strongly compact can be the least strong and indestructible.Arthur W. Apter - 2006 - Annals of Pure and Applied Logic 144 (1-3):33-42.
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Indestructibility, measurability, and degrees of supercompactness.Arthur W. Apter - 2012 - Mathematical Logic Quarterly 58 (1):75-82.
On a problem of Foreman and Magidor.Arthur W. Apter - 2005 - Archive for Mathematical Logic 44 (4):493-498.
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