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An Smax Variation for One Souslin Tree
The Journal of Symbolic Logic
Vol. 64, No. 1 (Mar., 1999), pp. 81-98
Published by: Association for Symbolic Logic
Stable URL: http://www.jstor.org/stable/2586753
Page Count: 18
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We present a variation of the forcing Smax as presented in Woodin . 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.
The Journal of Symbolic Logic © 1999 Association for Symbolic Logic