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March 2009 Increasing u2 by a stationary set preserving forcing
Benjamin Claverie, Ralf Schindler
J. Symbolic Logic 74(1): 187-200 (March 2009). DOI: 10.2178/jsl/1231082308

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.

Citation

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Benjamin Claverie. Ralf Schindler. "Increasing u2 by a stationary set preserving forcing." J. Symbolic Logic 74 (1) 187 - 200, March 2009. https://doi.org/10.2178/jsl/1231082308

Information

Published: March 2009
First available in Project Euclid: 4 January 2009

zbMATH: 1163.03026
MathSciNet: MR2499426
Digital Object Identifier: 10.2178/jsl/1231082308

Rights: Copyright © 2009 Association for Symbolic Logic

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Vol.74 • No. 1 • March 2009
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