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 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 [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.
John Krueger. "Fat sets and saturated ideals." J. Symbolic Logic 68 (3) 837 - 845, September 2003. https://doi.org/10.2178/jsl/1058448442