Bounded Martin's Maximum with Many Witnesses

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dc.creatorZoble, Stuart
dc.date2008-12-07
dc.date.accessioned2026-07-07T12:10:05Z
dc.date.available2026-07-07T12:10:05Z
dc.descriptionWe study a strengthening of Bounded Martin's Maximum which asserts that if a Σ_1 fact holds of ω_2^V in a stationary set preserving extension then it holds in V for a stationary set of ordinals less than ω_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 ω_2^V countably cofinal does hold in the \mathsf{BMM} model, though it is not a consequence of \mathsf{BMM}.
dc.identifierhttps://arxiv.org/abs/0812.1330
dc.identifierhttp://arxiv.org/abs/0812.1330
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/209839
dc.subjectLogic
dc.subject03E45
dc.titleBounded Martin's Maximum with Many Witnesses
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