When Pκ(λ) (vaguely) resembles κ

Abstract

Let μ<κ<λ be three infinite cardinals, the first two being regular. Assuming the existence of a cofinal subset of (Pκ(λ),⊆) of size λ, we define an ideal on Pκ(λ) which we argue to be the analog for Pκ(λ) of NSκ|Eμκ (the restriction of the nonstationary ideal on κ to the set of limit ordinals less than κ of cofinality μ). We show that this ideal on Pκ(λ) is the ideal dual to the well-known μ-club filter, thus answering a question raised by Krueger and Foreman.