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An Smax Variation for One Souslin Tree

Paul Larson
The Journal of Symbolic Logic
Vol. 64, No. 1 (Mar., 1999), pp. 81-98
DOI: 10.2307/2586753
Stable URL: http://www.jstor.org/stable/2586753
Page Count: 18
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An Smax Variation for One Souslin Tree
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Abstract

We present a variation of the forcing Smax as presented in Woodin [4]. Our forcing is a Pmax-style construction where each model condition selects one Souslin tree. In the extension there is a Souslin tree TG which is the direct limit of the selected Souslin trees in the models of the generic. In some sense, the generic extension is a maximal model of "there exists a minimal Souslin tree," with TG being this minimal tree. In particular, in the extension this Souslin tree has the property that forcing with it gives a model of Souslin's Hypothesis.

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