Fat sets and saturated ideals

Journal of Symbolic Logic 68 (3):837-845 (2003)

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 $NS_{\kappa} \upharpoonright S$ is saturated then $\kappa \S$ 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 $\lambda^{+++}-saturated$ normal ideal on $P_{\kappa} \lambda$ then the conditions of being $\lambda^{+}-preserving$ , weakly presaturated, and presaturated are equivalent for I
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DOI 10.2178/jsl/1058448442
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References found in this work BETA

[Omnibus Review].Thomas Jech - 1992 - Journal of Symbolic Logic 57 (1):261-262.
Forcing Closed Unbounded Sets.Uri Abraham & Saharon Shelah - 1983 - Journal of Symbolic Logic 48 (3):643-657.
Cardinal Arithmetic.Saharon Shelah - 1998 - Studia Logica 60 (3):443-448.

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Citations of this work BETA

In Memoriam: James Earl Baumgartner.J. A. Larson - 2017 - Archive for Mathematical Logic 56 (7-8):877-909.

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