Archive for Mathematical Logic 42 (8):717-735 (2003)

Abstract
.In this paper, we first prove several general theorems about strongness, supercompactness, and indestructibility, along the way giving some new applications of Hamkins’ lottery preparation forcing to indestructibility. We then show that it is consistent, relative to the existence of cardinals κ<λ so that κ is λ supercompact and λ is inaccessible, for the least strongly compact cardinal κ to be the least strong cardinal and to have its strongness, but not its strong compactness, indestructible under κ-strategically closed forcing.
Keywords Supercompact cardinal  Strongly compact cardinal  Strong cardinal  Lottery preparation  Indestructibility  Non-reflecting stationary set of ordinals
Categories (categorize this paper)
ISBN(s)
DOI 10.1007/s00153-003-0181-3
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 65,599
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

The Higher Infinite.Akihiro Kanamori - 2000 - Studia Logica 65 (3):443-446.
Strong Axioms of Infinity and Elementary Embeddings.Robert M. Solovay - 1978 - Annals of Mathematical Logic 13 (1):73.
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 10 references / Add more references

Citations of this work BETA

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.
Normal Measures on a Tall Cardinal.Arthur W. Apter & James Cummings - 2019 - Journal of Symbolic Logic 84 (1):178-204.

Add more citations

Similar books and articles

An Equiconsistency for Universal Indestructibility.Arthur W. Apter & Grigor Sargsyan - 2010 - Journal of Symbolic Logic 75 (1):314-322.
Indestructible Strong Compactness and Level by Level Inequivalence.Arthur W. Apter - 2013 - Mathematical Logic Quarterly 59 (4-5):371-377.
Indestructible Strong Unfoldability.Joel David Hamkins & Thomas A. Johnstone - 2010 - Notre Dame Journal of Formal Logic 51 (3):291-321.
On the Indestructibility Aspects of Identity Crisis.Grigor Sargsyan - 2009 - Archive for Mathematical Logic 48 (6):493-513.
Characterizing Strong Compactness Via Strongness.Arthur W. Apter - 2003 - Mathematical Logic Quarterly 49 (4):375.
Universal Partial Indestructibility and Strong Compactness.Arthur W. Apter - 2005 - Mathematical Logic Quarterly 51 (5):524-531.
Level by Level Inequivalence Beyond Measurability.Arthur W. Apter - 2011 - Archive for Mathematical Logic 50 (7-8):707-712.

Analytics

Added to PP index
2013-11-23

Total views
17 ( #621,992 of 2,462,142 )

Recent downloads (6 months)
1 ( #449,335 of 2,462,142 )

How can I increase my downloads?

Downloads

My notes