Fat sets and saturated ideals

Abstract

AbstractWe 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.