David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Symbolic Logic 64 (4):1675-1688 (1999)
We extend earlier work (both individual and joint with Shelah) and prove three theorems about the class of measurable limits of compact cardinals, where a compact cardinal is one which is either strongly compact or supercompact. In particular, we construct two models in which every measurable limit of compact cardinals below the least supercompact limit of supercompact cardinals possesses non-trivial degrees of supercompactness. In one of these models, every measurable limit of compact cardinals is a limit of supercompact cardinals and also a limit of strongly compact cardinals having no non-trivial degree of supercompactness. We also show that it is consistent for the least supercompact cardinal κ to be a limit of strongly compact cardinals and be so that every measurable limit of compact cardinals below κ has a non-trivial degree of supercompactness. In this model, the only compact cardinals below κ with a non-trivial degree of supercompactness are the measurable limits of compact cardinals
|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 & James Cummings (2000). Identity Crises and Strong Compactness. Journal of Symbolic Logic 65 (4):1895-1910.
Jouko Väänänen (1982). Abstract Logic and Set Theory. II. Large Cardinals. Journal of Symbolic Logic 47 (2):335-346.
Andrés Villaveces (1999). Heights of Models of ZFC and the Existence of End Elementary Extensions II. Journal of Symbolic Logic 64 (3):1111-1124.
Arthur W. Apter (1981). Measurability and Degrees of Strong Compactness. Journal of Symbolic Logic 46 (2):249-254.
Arthur W. Apter (2001). Supercompactness and Measurable Limits of Strong Cardinals. Journal of Symbolic Logic 66 (2):629-639.
Arthur W. Apter (2001). Some Structural Results Concerning Supercompact Cardinals. Journal of Symbolic Logic 66 (4):1919-1927.
Arthur W. Apter & Moti Gitik (1998). The Least Measurable Can Be Strongly Compact and Indestructible. Journal of Symbolic Logic 63 (4):1404-1412.
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 & Joel David Hamkins (2003). Exactly Controlling the Non-Supercompact Strongly Compact Cardinals. Journal of Symbolic Logic 68 (2):669-688.
Added to index2009-01-28
Total downloads8 ( #267,348 of 1,725,584 )
Recent downloads (6 months)1 ( #349,437 of 1,725,584 )
How can I increase my downloads?