Abstract
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. 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). On the other hand, PFA(S) implies there is a first-countable perfect pre-image of ω1 that contains no copies of ω1.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
