An smax variation for one souslin tree

Journal of Symbolic Logic 64 (1):81 - 98 (1999)
We present a variation of the forcing S max as presented in Woodin [4]. Our forcing is a P max -style construction where each model condition selects one Souslin tree. In the extension there is a Souslin tree T G 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 T G 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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DOI 10.2307/2586753
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Souslin Algebra Embeddings.Gido Scharfenberger-Fabian - 2011 - Archive for Mathematical Logic 50 (1-2):75-113.
The Grounded Martin's Axiom.Miha E. Habič - 2017 - Mathematical Logic Quarterly 63 (5):437-453.
A Microscopic Approach to Souslin-Tree Constructions, Part I.Ari Meir Brodsky & Assaf Rinot - 2017 - Annals of Pure and Applied Logic 168 (11):1949-2007.

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