Cofinal types on ω₂

2021/08/08 by Boriša Kuzeljević, Kuzeljevic, Borisa, Stevo Todorčević +1
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topology and Set Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2108.03701

openalex publication_date 2021/08/08 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

Abstract

In this paper we start the analysis of the class \mathcal D_ℵ2, the class of cofinal types of directed sets of cofinality at most ℵ₂. We compare elements of \mathcal D_ℵ2 using the notion of Tukey reducibility. We isolate some simple cofinal types in \mathcal D_ℵ2, and then proceed to show which of these types have an immediate successor in the Tukey ordering of \mathcal D_ℵ2.

Related

• Cofinal types below ℵ_ω
• Cofinal types and topological groups
• Commutativity of Cofinal Types
• Continuous and other finitely generated canonical cofinal maps on\n ultrafilters
• Tukey types of ultrafilters