## Logic Seminar

Jin Du

UIC

Diamond, Scales and SCH Down to $\aleph_{\omega^2}$

**Abstract:**Gitik and Rinot proved assuming the existence of a supercompact that it is consistent to have a strong limit cardinal $\kappa$ such that $2^\kappa=\kappa^+$, there is a very good scale at $\kappa$, and diamond fails along some reflecting stationary subset of $\kappa^+\cap \operatorname{cof}(\omega)$. I will force over Gitik and Rinot's model but with a modification to Gitik-Sharon diagonal Prikry forcing to get this result for $\kappa = \aleph_{\omega^2}$.

Tuesday September 12, 2017 at 4:00 PM in SEO 427