Characterizing strong compactness via strongness

Mathematical Logic Quarterly 49 (4):375 (2003)
  Copy   BIBTEX

Abstract

We construct a model in which the strongly compact cardinals can be non-trivially characterized via the statement “κ is strongly compact iff κ is a measurable limit of strong cardinals”. If our ground model contains large enough cardinals, there will be supercompact cardinals in the universe containing this characterization of the strongly compact cardinals

Categories

Keywords

Reprint years

DOI

10.1002/malq.200310040

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,349

External links

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

Through your library

My notes

Similar books and articles

Some remarks on indestructibility and Hamkins? lottery preparation.Arthur W. Apter - 2003 - Archive for Mathematical Logic 42 (8):717-735.
Indestructibility, instances of strong compactness, and level by level inequivalence.Arthur W. Apter - 2010 - Archive for Mathematical Logic 49 (7-8):725-741.
Level by level inequivalence beyond measurability.Arthur W. Apter - 2011 - Archive for Mathematical Logic 50 (7-8):707-712.
Supercompactness and level by level equivalence are compatible with indestructibility for strong compactness.Arthur W. Apter - 2007 - Archive for Mathematical Logic 46 (3-4):155-163.
Identity crises and strong compactness III: Woodin cardinals. [REVIEW]Arthur W. Apter & Grigor Sargsyan - 2006 - Archive for Mathematical Logic 45 (3):307-322.
Level by level equivalence and strong compactness.Arthur W. Apter - 2004 - Mathematical Logic Quarterly 50 (1):51.
Indestructible strong compactness and level by level inequivalence.Arthur W. Apter - 2013 - Mathematical Logic Quarterly 59 (4-5):371-377.
Failure of GCH and the level by level equivalence between strong compactness and supercompactness.Arthur W. Apter - 2003 - Mathematical Logic Quarterly 49 (6):587.
An equiconsistency for universal indestructibility.Arthur W. Apter & Grigor Sargsyan - 2010 - Journal of Symbolic Logic 75 (1):314-322.
Inner models with large cardinal features usually obtained by forcing.Arthur W. Apter, Victoria Gitman & Joel David Hamkins - 2012 - Archive for Mathematical Logic 51 (3-4):257-283.
Failures of SCH and Level by Level Equivalence.Arthur W. Apter - 2006 - Archive for Mathematical Logic 45 (7):831-838.
On some questions concerning strong compactness.Arthur W. Apter - 2012 - Archive for Mathematical Logic 51 (7-8):819-829.
Indestructibility and level by level equivalence and inequivalence.Arthur W. Apter - 2007 - Mathematical Logic Quarterly 53 (1):78-85.
Diamond, square, and level by level equivalence.Arthur W. Apter - 2005 - Archive for Mathematical Logic 44 (3):387-395.

Analytics

Added to PP
2013-12-01

Downloads
17 (#843,162)

6 months
3 (#1,023,809)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

On the indestructibility aspects of identity crisis.Grigor Sargsyan - 2009 - Archive for Mathematical Logic 48 (6):493-513.

Add more citations

References found in this work

Strong axioms of infinity and elementary embeddings.Robert M. Solovay - 1978 - Annals of Mathematical Logic 13 (1):73.
On strong compactness and supercompactness.Telis K. Menas - 1975 - Annals of Mathematical Logic 7 (4):327-359.
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.

View all 11 references / Add more references