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 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.