An variation for one souslin tree

Journal of Symbolic Logic 64 (1):81-98 (1999)

Abstract

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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References found in this work

Set Theory.Keith J. Devlin - 1981 - Journal of Symbolic Logic 46 (4):876-877.

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Citations of this work

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.
A Microscopic Approach to Souslin-Tree Construction, Part II.Ari Meir Brodsky & Assaf Rinot - 2021 - Annals of Pure and Applied Logic 172 (5):102904.
Saturation, Suslin Trees and Meager Sets.Paul Larson - 2005 - Archive for Mathematical Logic 44 (5):581-595.
Gap Structure After Forcing with a Coherent Souslin Tree.Carlos Martinez-Ranero - 2013 - Archive for Mathematical Logic 52 (3-4):435-447.
Souslin Algebra Embeddings.Gido Scharfenberger-Fabian - 2011 - Archive for Mathematical Logic 50 (1-2):75-113.

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