## 116b- Lecture 12

February 15, 2008

We sketched the method of indicators and the hierarchy of fast-growing functions as techniques to prove independence in $\mathsf{PA}$. Then we proved Ramsey’s theorem. We will use the method of indicators to show the Kanamori-McAloon theorem that the version of Ramsey’s theorem for regressive functions is not provable in $\mathsf{PA}$.