Journal of Symbolic Logic 68 (2):669-688 (2003)
|Abstract||We summarize the known methods of producing a non-supercompact strongly compact cardinal and describe some new variants. Our Main Theorem shows how to apply these methods to many cardinals simultaneously and exactly control which cardinals are supercompact and which are only strongly compact in a forcing extension. Depending upon the method, the surviving non-supercompact strongly compact cardinals can be strong cardinals, have trivial Mitchell rank or even contain a club disjoint from the set of measurable cardinals. These results improve and unify Theorems 1 and 2 of , due to the first author|
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
|Through your library||Configure|
Similar books and articles
Ralf-Dieter Schindler (1999). Successive Weakly Compact or Singular Cardinals. Journal of Symbolic Logic 64 (1):139-146.
Yoshihiro Abe (1985). Some Results Concerning Strongly Compact Cardinals. Journal of Symbolic Logic 50 (4):874-880.
Arthur W. Apter (1981). Measurability and Degrees of Strong Compactness. Journal of Symbolic Logic 46 (2):249-254.
Jouko Väänänen (1982). Abstract Logic and Set Theory. II. Large Cardinals. Journal of Symbolic Logic 47 (2):335-346.
Arthur W. Apter & James Cummings (2000). Identity Crises and Strong Compactness. Journal of Symbolic Logic 65 (4):1895-1910.
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 (2001). Some Structural Results Concerning Supercompact Cardinals. Journal of Symbolic Logic 66 (4):1919-1927.
Joel David Hamkins (1999). Gap Forcing: Generalizing the Lévy-Solovay Theorem. Bulletin of Symbolic Logic 5 (2):264-272.
Arthur W. Apter (1998). Laver Indestructibility and the Class of Compact Cardinals. Journal of Symbolic Logic 63 (1):149-157.
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 ( #245,513 of 722,698 )
Recent downloads (6 months)1 ( #60,006 of 722,698 )
How can I increase my downloads?