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Pκλ combinatorics II: The RK ordering beneath a supercompact measure

Published online by Cambridge University Press:  12 March 2014

William S. Zwicker
William S. Zwicker*
Affiliation:
Department of Mathematics, Union College, Schenectady, New York 12308
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Abstract

We characterize some large cardinal properties, such as μ-measurability and P2(κ)-measurability, in terms of ultrafilters, and then explore the Rudin-Keisler (RK) relations between these ultrafilters and supercompact measures on Pκ(2κ). This leads to the characterization of 2κ-supercompactness in terms of a measure on measure sequences, and also to the study of a certain natural subset, Fullκ, of Pκ(2κ) whose elements code measures on cardinals less than κ. The hypothesis that Fullκ is stationary (a weaker assumption than 2κ-supercompactness) is equivalent to a higher order Löwenheim-Skolem property, and settles a question about directed versus chain-type unions on Pκλ.

Keywords

PκλhypermeasurablesupercompactLöwenheim-Skolem theorem.
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 51 , Issue 3 , September 1986 , pp. 604 - 616
Copyright
Copyright © Association for Symbolic Logic 1986

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References

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