## 116c- Lecture 11

We proved Fodor’s theorem and showed some of its consequences.

We also proved Ulam’s theorem that any stationary subset of a successor cardinal $\kappa^+$ can be partitioned into $\kappa^+$ disjoint stationary sets. This result also holds for limit regular cardinals $\lambda$, with a more elaborate proof that is sketched in the new homework set.

We then started the proof of Silver’s theorem that $\aleph_{\omega_1}$ is not the first counterexample to ${\sf GCH}$.