Increasing u2 by a stationary set preserving forcing
Keyword(s):
AbstractWe show that if I is a precipitous ideal on ω1 and if θ > ω1 is a regular cardinal, then there is a forcing ℙ = ℙ(I, θ) which preserves the stationarity of all I-positive sets such that in Vℙ, ⟨Hθ; ∈, I⟩ is a generic iterate of a countable structure ⟨M; ∈, Ī⟩. This shows that if the nonstationary ideal on ω1 is precipitous and exists, then there is a stationary set preserving forcing which increases . Moreover, if Bounded Martin's Maximum holds and the nonstationary ideal on ω1 is precipitous, then .
1989 ◽
Vol 40
(3)
◽
pp. 381-387
Keyword(s):
Keyword(s):
Keyword(s):
Keyword(s):
2005 ◽
Vol 357
(12)
◽
pp. 4813-4837
◽
Keyword(s):