Joint work with Roy Shalev.
Abstract. We introduce a new combinatorial principle which we call . 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 follow from the existence of a Souslin tree. It is also shown that the weakest instance of 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 -space which is Dowker.
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Submitted to Topology and its Applications, October 2020.
Accepted, September 2021.
In an upcoming paper, we answer Question 2.35 in the negative. Furthermore, we prove that the existence of a Luzin set implies