Abstract
AbstractWe show that L(ℝ) absoluteness for semi‐proper forcings is equiconsistent with the existence of a remarkable cardinal, and hence by [6] with L(ℝ) absoluteness for proper forcings. By [7], L(ℝ) absoluteness for stationary set preserving forcings gives an inner model with a strong cardinal. By [3], the Bounded Semi‐Proper Forcing Axiom (BSPFA) is equiconsistent with the Bounded Proper Forcing Axiom (BPFA), which in turn is equiconsistent with a reflecting cardinal. We show that Bounded Martin's Maximum (BMM) is much stronger than BSPFA in that if BMM holds, then for every X ∈ V , X# exists. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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.
