Bounded Martin's Maximum with Many Witnesses
Logic
2008-12-09 v1
Abstract
We study a strengthening of Bounded Martin's Maximum which asserts that if a \Sigma_1 fact holds of \omega_2^V in a stationary set preserving extension then it holds in V for a stationary set of ordinals less than \omega_2. We show that this principle implies Global Projective Determinacy, and therefore does not hold in the \mathbb{P}_{max} model for \mathsf{BMM}, but that the restriction of this principle to forcings which render \omega_2^V countably cofinal does hold in the \mathsf{BMM} model, though it is not a consequence of \mathsf{BMM}.
Cite
@article{arxiv.0812.1330,
title = {Bounded Martin's Maximum with Many Witnesses},
author = {Stuart Zoble},
journal= {arXiv preprint arXiv:0812.1330},
year = {2008}
}