Strongly unfoldable cardinals made indestructible

Journal of Symbolic Logic 73 (4):1215-1248 (2008)

Abstract

I provide indestructibility results for large cardinals consistent with V = L, such as weakly compact, indescribable and strongly unfoldable cardinals. The Main Theorem shows that any strongly unfoldable cardinal κ can be made indestructible by <κ-closed. κ-proper forcing. This class of posets includes for instance all <κ-closed posets that are either κ -c.c, or ≤κ-strategically closed as well as finite iterations of such posets. Since strongly unfoldable cardinals strengthen both indescribable and weakly compact cardinals, the Main Theorem therefore makes these two large cardinal notions similarly indestructible. Finally. I apply the Main Theorem forcing extension preserving all strongly unfoldable cardinals in which every strongly unfoldable cardinal κ is indestructible by <κ-closed. κ-proper forcing

Download options

PhilArchive



    Upload a copy of this work     Papers currently archived: 72,891

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Analytics

Added to PP
2010-09-12

Downloads
26 (#444,425)

6 months
1 (#386,040)

Historical graph of downloads
How can I increase my downloads?

References found in this work

The Lottery Preparation.Joel David Hamkins - 2000 - Annals of Pure and Applied Logic 101 (2-3):103-146.

Add more references

Similar books and articles

Unfoldable Cardinals and the GCH.Joel David Hamkins - 2001 - Journal of Symbolic Logic 66 (3):1186-1198.
Indestructible Strong Unfoldability.Joel David Hamkins & Thomas A. Johnstone - 2010 - Notre Dame Journal of Formal Logic 51 (3):291-321.
Chains of End Elementary Extensions of Models of Set Theory.Andrés Villaveces - 1998 - Journal of Symbolic Logic 63 (3):1116-1136.
Small Forcing Makes Any Cardinal Superdestructible.Joel David Hamkins - 1998 - Journal of Symbolic Logic 63 (1):51-58.
On Measurable Limits of Compact Cardinals.Arthur W. Apter - 1999 - Journal of Symbolic Logic 64 (4):1675-1688.
Gap Forcing: Generalizing the Lévy-Solovay Theorem.Joel David Hamkins - 1999 - Bulletin of Symbolic Logic 5 (2):264-272.
Some Results Concerning Strongly Compact Cardinals.Yoshihiro Abe - 1985 - Journal of Symbolic Logic 50 (4):874-880.
Core Models in the Presence of Woodin Cardinals.Ralf Schindler - 2006 - Journal of Symbolic Logic 71 (4):1145 - 1154.
Some Structural Results Concerning Supercompact Cardinals.Arthur W. Apter - 2001 - Journal of Symbolic Logic 66 (4):1919-1927.