Cofinal types on ω2

Pub Date : 2023-05-31 DOI:10.1002/malq.202200021

Borisa Kuzeljevic, Stevo Todorcevic

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引用次数: 3

Abstract

In this paper we start the analysis of the class $D_{ℵ_{2}}$ , the class of cofinal types of directed sets of cofinality at most ℵ₂. We compare elements of $D_{ℵ_{2}}$ using the notion of Tukey reducibility. We isolate some simple cofinal types in $D_{ℵ_{2}}$ , and then proceed to find some of these types which have an immediate successor in the Tukey ordering of $D_{ℵ_{2}}$ .

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ω2上的共尾型

在本文中，我们开始分析D类ℵ 2$\mathcal{D}_｛\aleph_2｝$，至多有向共尾集的一类共尾类型ℵ2.我们比较D的元素ℵ 2$\mathcal{D}_｛\aleph_2｝$使用Tukey可约性的概念。我们在D中分离出一些简单的共尾类型ℵ 2$\mathcal{D}_｛\aleph_2｝$，然后继续寻找其中一些在D的Tukey排序中具有直接后继的类型ℵ 2$\mathcal{D}_｛\alph_2｝$。

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