David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Symbolic Logic 63 (1):149-157 (1998)
Using an idea developed in joint work with Shelah, we show how to redefine Laver's notion of forcing making a supercompact cardinal κ indestructible under κ-directed closed forcing to give a new proof of the Kimchi-Magidor Theorem in which every compact cardinal in the universe (supercompact or strongly compact) satisfies certain indestructibility properties. Specifically, we show that if K is the class of supercompact cardinals in the ground model, then it is possible to force and construct a generic extension in which the only strongly compact cardinals are the elements of K or their measurable limit points, every κ ∈ K is a supercompact cardinal indestructible under κ-directed closed forcing, and every κ a measurable limit point of K is a strongly compact cardinal indestructible under κ-directed closed forcing not changing ℘(κ). We then derive as a corollary a model for the existence of a strongly compact cardinal κ which is not κ + supercompact but which is indestructible under κ-directed closed forcing not changing ℘(κ) and remains non-κ + supercompact after such a forcing has been done
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
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
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Arthur W. Apter & Joel David Hamkins (2002). Indestructibility and the Level-by-Level Agreement Between Strong Compactness and Supercompactness. Journal of Symbolic Logic 67 (2):820-840.
Paul Corazza (1999). Laver Sequences for Extendible and Super-Almost-Huge Cardinals. Journal of Symbolic Logic 64 (3):963-983.
Joel David Hamkins (2001). Unfoldable Cardinals and the GCH. Journal of Symbolic Logic 66 (3):1186-1198.
Arthur W. Apter & James Cummings (2000). Identity Crises and Strong Compactness. Journal of Symbolic Logic 65 (4):1895-1910.
Arthur W. Apter (2001). Some Structural Results Concerning Supercompact Cardinals. Journal of Symbolic Logic 66 (4):1919-1927.
Joel David Hamkins (1998). Small Forcing Makes Any Cardinal Superdestructible. Journal of Symbolic Logic 63 (1):51-58.
Joel David Hamkins (1999). Gap Forcing: Generalizing the Lévy-Solovay Theorem. Bulletin of Symbolic Logic 5 (2):264-272.
Arthur W. Apter & Joel David Hamkins (2003). Exactly Controlling the Non-Supercompact Strongly Compact Cardinals. Journal of Symbolic Logic 68 (2):669-688.
Arthur W. Apter & Moti Gitik (1998). The Least Measurable Can Be Strongly Compact and Indestructible. Journal of Symbolic Logic 63 (4):1404-1412.
Arthur W. Apter (1999). On Measurable Limits of Compact Cardinals. Journal of Symbolic Logic 64 (4):1675-1688.
Added to index2009-01-28
Total downloads2 ( #412,272 of 1,692,590 )
Recent downloads (6 months)1 ( #181,202 of 1,692,590 )
How can I increase my downloads?