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

We introduce a new combinatorial principle which we call ♣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...

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Bibliographic Details
Published in:Topology and its applications 2023-01, Vol.323, p.108296, Article 108296
Main Authors: Rinot, Assaf, Shalev, Roy
Format: Article
Language:English
Subjects:
Almost disjoint
Club
Dowker space
Ostaszewski space
Souslin line
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Summary:We introduce a new combinatorial principle which we call ♣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 ♣AD follow from the existence of a Souslin tree. It is also shown that the weakest instance of ♣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.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2022.108296