An $\mathbb{S}_{max}$ Variation for One Souslin Tree
Larson, Paul
J. Symbolic Logic, Tome 64 (1999) no. 1, p. 81-98 / Harvested from Project Euclid
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.
Publié le : 1999-03-14
Classification: 
@article{1183745694,
     author = {Larson, Paul},
     title = {An $\mathbb{S}\_{max}$ Variation for One Souslin Tree},
     journal = {J. Symbolic Logic},
     volume = {64},
     number = {1},
     year = {1999},
     pages = { 81-98},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183745694}
}
Larson, Paul. An $\mathbb{S}_{max}$ Variation for One Souslin Tree. J. Symbolic Logic, Tome 64 (1999) no. 1, pp.  81-98. http://gdmltest.u-ga.fr/item/1183745694/