### Increasing u2 by a stationary set preserving forcing

Benjamin Claverie and Ralf Schindler
Source: J. Symbolic Logic Volume 74, Issue 1 (2009), 187-200.

#### Abstract

We show that if I is a precipitous ideal on ω1 and if θ > ω1 is a regular cardinal, then there is a forcing ℛ = ℛ(I,θ) which preserves the stationarity of all I-positive sets such that in V, 〈 Hθ;∈,I 〉 is a generic iterate of a countable structure 〈 M;∈,Ī 〉. This shows that if the nonstationary ideal on ω1 is precipitous and Hθ# exists, then there is a stationary set preserving forcing which increases \utilde{δ}12. Moreover, if Bounded Martin's Maximum holds and the nonstationary ideal on ω1 is precipitous, then \utilde{δ}12 = u2 = ω2.

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Permanent link to this document: http://projecteuclid.org/euclid.jsl/1231082308
Digital Object Identifier: doi:10.2178/jsl/1231082308
Mathematical Reviews number (MathSciNet): MR2499426

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