Analytic ideals and cofinal types

Abstract

We study the class of analytic ideals on the set of natural numbers ordered under Tukey reducibility. We consider mostly structural issues: characterization of ideals which are Tukey above ω ω , extremal elements for the class of analytic P-ideals, etc. We prove that this class is very rich by embedding into it (℘( N ), ⊆ ∗). We also study ideals associated to classical Banach spaces and ideals of compacts sets in a Polish space.