116c- Lecture 11

May 6, 2008

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}.