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
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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.
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References found in this work

The Higher Infinite.Akihiro Kanamori - 2000 - Studia Logica 65 (3):443-446.
Set Theory.Jouko Vaananen - 2010 - Journal of the Indian Council of Philosophical Research 27 (1).
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.
Destruction or preservation as you like it.Joel David Hamkins - 1998 - Annals of Pure and Applied Logic 91 (2-3):191-229.

View all 8 references / Add more references