David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Symbolic Logic 51 (3):604 - 616 (1986)
We characterize some large cardinal properties, such as μ-measurability and P 2 (κ)-measurability, in terms of ultrafilters, and then explore the Rudin-Keisler (RK) relations between these ultrafilters and supercompact measures on P κ (2 κ ). This leads to the characterization of 2 κ -supercompactness in terms of a measure on measure sequences, and also to the study of a certain natural subset, Full κ , of P κ (2 κ ), whose elements code measures on cardinals less than κ. The hypothesis that Full κ is stationary (a weaker assumption than 2 κ -supercompactness) is equivalent to a higher order Lowenheim-Skolem property, and settles a question about directed versus chain-type unions on P κ λ
|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 (1998). Laver Indestructibility and the Class of Compact Cardinals. Journal of Symbolic Logic 63 (1):149-157.
Andreas Blass (1981). Some Initial Segments of the Rudin-Keisler Ordering. Journal of Symbolic Logic 46 (1):147-157.
Itay Neeman (2007). Inner Models and Ultrafilters in L(R). Bulletin of Symbolic Logic 13 (1):31-53.
Michael Benedikt (1998). Ultrafilters Which Extend Measures. Journal of Symbolic Logic 63 (2):638-662.
Julius B. Barbanel (1992). A Note on a Result of Kunen and Pelletier. Journal of Symbolic Logic 57 (2):461-465.
Arthur W. Apter (2001). Some Structural Results Concerning Supercompact Cardinals. Journal of Symbolic Logic 66 (4):1919-1927.
Arthur W. Apter (1999). On Measurable Limits of Compact Cardinals. Journal of Symbolic Logic 64 (4):1675-1688.
Julius B. Barbanel (1986). Supercompact Cardinals, Trees of Normal Ultrafilters, and the Partition Property. Journal of Symbolic Logic 51 (3):701-708.
Kenneth Kunen & Donald H. Pelletier (1983). On a Combinatorial Property of Menas Related to the Partition Property for Measures on Supercompact Cardinals. Journal of Symbolic Logic 48 (2):475-481.
Julius B. Barbanel (1993). On the Relationship Between the Partition Property and the Weak Partition Property for Normal Ultrafilters on Pκλ. Journal of Symbolic Logic 58 (1):119 - 127.
Added to index2009-01-28
Total downloads6 ( #290,652 of 1,696,463 )
Recent downloads (6 months)4 ( #140,936 of 1,696,463 )
How can I increase my downloads?