Small Forcing Makes any Cardinal Superdestructible

Journal of Symbolic Logic 63 (1):51-58 (1998)
  Copy   BIBTEX

Abstract

Small forcing always ruins the indestructibility of an indestructible supercompact cardinal. In fact, after small forcing, any cardinal $\kappa$ becomes superdestructible--any further <$\kappa$--closed forcing which adds a subset to $\kappa$ will destroy the measurability, even the weak compactness, of $\kappa$. Nevertheless, after small forcing indestructible cardinals remain resurrectible, but never strongly resurrectible.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 90,616

External links

  • This entry has no external links. Add one.
Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Small forcing makes any cardinal superdestructible.Joel David Hamkins - 1998 - Journal of Symbolic Logic 63 (1):51-58.
Laver Indestructibility and the Class of Compact Cardinals.Arthur W. Apter - 1998 - Journal of Symbolic Logic 63 (1):149-157.
The lottery preparation.Joel David Hamkins - 2000 - Annals of Pure and Applied Logic 101 (2-3):103-146.
Universal partial indestructibility and strong compactness.Arthur W. Apter - 2005 - Mathematical Logic Quarterly 51 (5):524-531.
Unfoldable Cardinals and the GCH.Joel Hamkins - 2001 - Journal of Symbolic Logic 66 (3):1186-1198.
Indestructibility and stationary reflection.Arthur W. Apter - 2009 - Mathematical Logic Quarterly 55 (3):228-236.
Partial near supercompactness.Jason Aaron Schanker - 2013 - Annals of Pure and Applied Logic 164 (2):67-85.
Large Cardinals and Large Dilators.Andy Lewis - 1998 - Journal of Symbolic Logic 63 (4):1496-1510.
Strongly unfoldable cardinals made indestructible.Thomas A. Johnstone - 2008 - Journal of Symbolic Logic 73 (4):1215-1248.
Tall cardinals.Joel D. Hamkins - 2009 - Mathematical Logic Quarterly 55 (1):68-86.
Indestructible Strong Unfoldability.Joel David Hamkins & Thomas A. Johnstone - 2010 - Notre Dame Journal of Formal Logic 51 (3):291-321.

Analytics

Added to PP
2017-02-21

Downloads
7 (#1,201,127)

6 months
6 (#202,901)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Joel David Hamkins
Oxford University

Citations of this work

Gap forcing: Generalizing the lévy-Solovay theorem.Joel David Hamkins - 1999 - Bulletin of Symbolic Logic 5 (2):264-272.
Indestructibility and destructible measurable cardinals.Arthur W. Apter - 2016 - Archive for Mathematical Logic 55 (1-2):3-18.
Fresh subsets of ultrapowers.Assaf Shani - 2016 - Archive for Mathematical Logic 55 (5-6):835-845.

Add more citations

References found in this work

No references found.

Add more references