Cofinal types on $omega_2$


Abstract in English

In this paper we start the analysis of the class $mathcal D_{aleph_2}$, the class of cofinal types of directed sets of cofinality at most $aleph_2$. We compare elements of $mathcal D_{aleph_2}$ using the notion of Tukey reducibility. We isolate some simple cofinal types in $mathcal D_{aleph_2}$, and then proceed to show which of these types have an immediate successor in the Tukey ordering of $mathcal D_{aleph_2}$.

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