## Journal of Symbolic Logic

### An $\mathbb{S}_{max}$ Variation for One Souslin Tree

Paul Larson

#### Abstract

We present a variation of the forcing $\mathbb{S}_{max}$ as presented in Woodin [4]. Our forcing is a $\mathbb{P}_{max}$-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.

#### Article information

Source
J. Symbolic Logic, Volume 64, Issue 1 (1999), 81-98.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183745694

Mathematical Reviews number (MathSciNet)
MR1683897

Zentralblatt MATH identifier
0926.03061

JSTOR
Larson, Paul. An $\mathbb{S}_{max}$ Variation for One Souslin Tree. J. Symbolic Logic 64 (1999), no. 1, 81--98. https://projecteuclid.org/euclid.jsl/1183745694