Analytic ideals and cofinal types Original Research Article

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 ωω, extremal elements for the class of analytic P-ideals, etc. We prove that this class is very rich by embedding into it (℘(View the MathML source), ⊆∗). We also study ideals associated to classical Banach spaces and ideals of compacts sets in a Polish space.