An variation for one souslin tree
Paul Larson · Journal of Symbolic Logic · 1999
Abstract We present a variation of the forcing 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.