Abstract
In this paper we show that the Proper Forcing Axiom (PFA) is preserved under forcing over any poset P with the following property: In the generalized Banach–Mazur game over P of length (ω1+1), Player II has a winning strategy which depends only on the current position and the ordinal indicating the number of moves made so far. By the current position we mean: The move just made by Player I for a successor stage, or the infimum of all the moves made so far for a limit stage. As a consequence of this theorem, we introduce a weak form of the square principle and show that it is consistent with PFA.
Sign-in/Register to access full text options 
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.
