Cofinal types on ω2

Abstract

In this paper we start the analysis of the class (Formula presented.), the class of cofinal types of directed sets of cofinality at most ℵ2. We compare elements of (Formula presented.) using the notion of Tukey reducibility. We isolate some simple cofinal types in (Formula presented.), and then proceed to find some of these types which have an immediate successor in the Tukey ordering of (Formula presented.).