Bounded Martin's Maximum with Many Witnesses

Publication date: 7 December 2008

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}.

Mathematics Subject Classification ID

Inner models, including constructibility, ordinal definability, and core models (03E45)

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