Mathematics – Logic
Scientific paper
2008-12-07
Mathematics
Logic
Scientific paper
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}.
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