Π2 consequences of BMM + NSω1 is precipitous and the semiproperness of stationary set preserving forcings. (English summary) Math. Res. Lett. 16 (2009), no. 5, 797–815. Summary: “We investigate which Π2 sentences (over Hω2) that are consequences of MM also follow from BMM + NSω1 is precipitous. It turns out that admissible club guessing (acg), δ 1 2 ω2, the club bounding principle (CBP), and ψAC as well as ϕAC follow from this weaker theory. 1 This was known for δ 2 = ω2 and ψAC but not for ϕAC and acg. Additionally we show that if for all regular θ ≥ ω2 there is a semiproper partial ordering that adds a generic iteration of length ω1 with last model Hθ, then all stationary set preserving forcings are semiproper.
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