A guessing principle from a Souslin tree, with applications to topology

2021/04/19 by Assaf Rinot, Rinot, Assaf, Roy Shalev +1
Mathematics · #03E65 #54G20 #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Mathematical Dynamics and Fractals #Primary 03E05 #Secondary 03E35

paper · pdf · doi:10.48550/arxiv.2104.09150

openalex publication_date 2021/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a new combinatorial principle which we call \clubsuit_AD. This principle asserts the existence of a certain multi-ladder system with guessing and almost-disjointness features, and is shown to be sufficient for carrying out de Caux type constructions of topological spaces. Our main result states that strong instances of \clubsuit_AD follow from the existence of a Souslin tree. It is also shown that the weakest instance of \clubsuit_AD does not follow from the existence of an almost Souslin tree. As an application, we obtain a simple, de Caux type proof of Rudin's result that if there is a Souslin tree, then there is an S-space which is Dowker.

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