Indestructibility and the level-by-level agreement between strong compactness and supercompactness

Journal of Symbolic Logic 67 (2):820-840 (2002)
Abstract
Can a supercompact cardinal κ be Laver indestructible when there is a level-by-level agreement between strong compactness and supercompactness? In this article, we show that if there is a sufficiently large cardinal above κ, then no, it cannot. Conversely, if one weakens the requirement either by demanding less indestructibility, such as requiring only indestructibility by stratified posets, or less level-by-level agreement, such as requiring it only on measure one sets, then yes, it can
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.2178/jsl/1190150111
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history
Request removal from index
Download options
Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 26,188
Through your library
References found in this work BETA
The Lottery Preparation.Joel David Hamkins - 2000 - Annals of Pure and Applied Logic 101 (2-3):103-146.
Destruction or Preservation as You Like It.Joel David Hamkins - 1998 - Annals of Pure and Applied Logic 91 (2-3):191-229.
Identity Crises and Strong Compactness.Arthur W. Apter & James Cummings - 2001 - Archive for Mathematical Logic 40 (1):25-38.

Add more references

Citations of this work BETA
Failures of SCH and Level by Level Equivalence.Arthur W. Apter - 2006 - Archive for Mathematical Logic 45 (7):831-838.
The Failure of GCH at a Degree of Supercompactness.Brent Cody - 2012 - Mathematical Logic Quarterly 58 (1):83-94.
Indestructibility, HOD, and the Ground Axiom.Arthur W. Apter - 2011 - Mathematical Logic Quarterly 57 (3):261-265.

Add more citations

Similar books and articles
On Measurable Limits of Compact Cardinals.Arthur W. Apter - 1999 - Journal of Symbolic Logic 64 (4):1675-1688.
Level Compactness.Gillman Payette & Blaine D'Entremont - 2006 - Notre Dame Journal of Formal Logic 47 (4):545-555.
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.
Two Concepts of Agreement.Christian List - 2002 - The Good Society 11 (1):72-79.
Supercompactness and Measurable Limits of Strong Cardinals.Arthur W. Apter - 2001 - Journal of Symbolic Logic 66 (2):629-639.
Measurability and Degrees of Strong Compactness.Arthur W. Apter - 1981 - Journal of Symbolic Logic 46 (2):249-254.
Representing High-Level Properties in Perceptual Experience.Parker Crutchfield - 2011 - Philosophical Psychology 25 (2):279 - 294.

Monthly downloads

Added to index

2009-01-28

Total downloads

28 ( #179,106 of 2,153,834 )

Recent downloads (6 months)

1 ( #398,274 of 2,153,834 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Order:
There  are no threads in this forum
Nothing in this forum yet.

Other forums