We give a new characterization of the nonstationary ideal on \\) in the case when \ is a regular uncountable cardinal and \ a singular strong limit cardinal of cofinality at least \.

Using previous work of Baumgartner, Shelah and others, we describe, for each infinite cardinal θκ, the smallest κ-normal ideal J on Pκ such that.

Given a regular infinite cardinal κ and a cardinal λ > κ, we study fine ideals H on Pκ that satisfy the square brackets partition relation equation image, where μ is a cardinal ≥2.