Cofinal types on $\omega_2$

Borisa Kuzeljevic; Stevo Todorcevic

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arXiv · 2108.03701

Cofinal types on $\omega_2$

Borisa Kuzeljevic·Stevo Todorcevic

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Abstract

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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BibTeX RIS

Borisa Kuzeljevic, Stevo Todorcevic. 2021-08-08. Cofinal types on $\omega_2$. https://arxiv.org/abs/2108.03701

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