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Fat sets and saturated ideals

Published online by Cambridge University Press:  12 March 2014

John Krueger
John Krueger*
Affiliation:
Department of Mathematical Sciences, Carnegie Mellon University, 5000 Forbes Ave. Pittsburgh, Pennsylvania 15213, USA, E-mail: jkrueger@andrew.cmu.edu, URL: http://www.andrew.cmu.edu/~jkrueger
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Abstract

We strengthen a theorem of Gitik and Shelah [6] by showing that if κ is either weakly inaccessible or the successor of a singular cardinal and S is a stationary subset of κ such that NSκ↾S is saturated then κ ∖ S is fat. Using this theorem we derive some results about the existence of fat stationary sets. We then strengthen some results due to Baumgartner and Taylor [2], showing in particular that if I is a λ+++-saturated normal ideal on Pκλ then the conditions of being λ+-preserving, weakly presaturated, and presaturated are equivalent for I.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 68 , Issue 3 , September 2003 , pp. 837 - 845
Copyright
Copyright © Association for Symbolic Logic 2003

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References

REFERENCES

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