Journal of Symbolic Logic

Fat sets and saturated ideals

John Krueger

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We strengthen a theorem of Gitik and Shelah [GS] 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 NSκS 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 [BT], showing in particular that if I is a λ+++-saturated normal ideal on Pκ λ then the conditions of being λ+-preserving, weakly presaturated, and presaturated are equivalent for I.

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J. Symbolic Logic, Volume 68, Issue 3 (2003), 837- 845.

First available in Project Euclid: 17 July 2003

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Krueger, John. Fat sets and saturated ideals. J. Symbolic Logic 68 (2003), no. 3, 837-- 845. doi:10.2178/jsl/1058448442.

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