Π 2 Consequences of BMM + NS ω 1 is precipitous and the semiproperness of stationary set preserving forcings

نویسندگان

  • Philipp Doebler
  • Ralf Schindler
چکیده

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 e12 = ω2, the club bounding principle (CBP), and ψAC as well as φAC follow from this weaker theory. This was known for δ e12 = 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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تاریخ انتشار 2009