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Fat sets and saturated ideals.
| Content Provider | CiteSeerX |
|---|---|
| Author | Krueger, John |
| Abstract | 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. §1. Introduction. In this paper we strengthen several known theorems about saturated and presaturated ideals, and present some results about the existence of fat stationary sets. One of the better known results in the area of saturated ideals is the following theorem of Gitik and Shelah [6]: if θ < θ + < κ are regular cardinals then NSκ ↾ cof(θ) is not saturated. This theorem solved the problem |
| File Format | |
| Access Restriction | Open |
| Subject Keyword | Fat Set Saturated Ideal Fat Stationary Set N Cof Singular Cardinal Saturated Normal Ideal Regular Cardinal Weakly Inaccessible Stationary Subset Saturated Ideal Following Theorem |
| Content Type | Text |
| Resource Type | Article |
