Indestructible Weakly Compact Cardinals and the Necessity of Supercompactness for Certain Proof Schemata

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Mathematical Logic Quarterly 47 (4):563-572 (2001)
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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 schemata

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10.1002/1521-3870(200111)47:4

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Joel David Hamkins
Oxford University

Citations of this work

Indestructible Strong Unfoldability.Joel David Hamkins & Thomas A. Johnstone - 2010 - Notre Dame Journal of Formal Logic 51 (3):291-321.
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The envelope of a pointclass under a local determinacy hypothesis.Trevor M. Wilson - 2015 - Annals of Pure and Applied Logic 166 (10):991-1018.
On a problem of Foreman and Magidor.Arthur W. Apter - 2005 - Archive for Mathematical Logic 44 (4):493-498.

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