AD${}^{+}$ implies that ${\omega }_1$ is a $\Theta$-Berkeley cardinal

Douglas Blue, Grigor Sargsyan

Following \cite{bagaria2019large}, given cardinals $\kappa <\lambda$, we say $\kappa$ is a club $\lambda$-Berkeley cardinal if for every transitive set $N$ of size $<\lambda$ such that $\kappa \subseteq N$, there is…