Pfa(s) and Countable Tightness

Todorcevic introduced the forcing axiom PFA(S) and established many consequences. We contribute to this project. In particular, we consider status under PFA(S) of two important consequences of PFA concerning spaces of countable tightness. In particular we prove that the existence of a Souslin tree does not imply the existence of a compact non-sequential space of countable tightness. We contrast this with M. E. Rudin’s result that the existence of a Souslin tree does imply the existence of an S-space (and the later improvement by Dahrough to a compact S-space).