Trees and stationary reflection at double successors of regular cardinals

2021/03/29 by Thomas Gilton, Gilton, Thomas, Maxwell Levine +3
Computer Science · Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2103.15728

openalex publication_date 2021/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain an array of consistency results concerning trees and stationary reflection at double successors of regular cardinals κ, updating some classical constructions in the process. This includes models of CSR(κ⁺⁺)\wedge TP(κ⁺⁺) (both with and without AP(κ⁺⁺)) and models of the conjunctions SR(κ⁺⁺) \wedge wTP(κ⁺⁺) \wedge AP(κ⁺⁺) and ¬ AP(κ⁺⁺) \wedge SR(κ⁺⁺) (the latter was originally obtained in joint work by Krueger and the first author \citeGilKru:8fold, and is here given using different methods). Analogs of these results with the failure of SH(κ⁺⁺) are given as well. Finally, we obtain all of our results with an arbitrarily large 2^κ, applying recent joint work by Honzik and the third author.

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