Forcing Seminar (Tel-Aviv University)
Tuesday, 29/Mar/2016, 9-11.
Room 209, Schriber building, Tel-Aviv University.
Speaker: Assaf Rinot
Title: The strength of the generalized Souslin hypothesis
Abstract: The goal of this talk is check my proof that GCH+$\square(\lambda^+)$ entails a $\lambda^+$-Souslin tree for every uncountable cardinal $\lambda$. If no errors are found, this shows that if GCH holds and there are no $\aleph_2$-Souslin trees, then $\aleph_2$ is weakly compact in $L$, improving upon Gregory’s 1976 lower bound (=Mahlo cardinal). Likewise, if GCH holds and there are no $\aleph_2$ and $\aleph_3$ Souslin trees, then the Axiom of Determinacy holds in $L(\mathbb R)$