Mitchell's Theorem Revisited

Abstract

Mitchell's theorem on the approachability ideal states that it is consistent relative to a greatly Mahlo cardinal that there is no stationary subset of ${\omega }_2\cap \mathrm{cof}({\omega }_1)$ in the approachability ideal $I[{\omega }_2]$. In this paper we give a new proof of Mitchell's theorem, deriving it from an abstract framework of side condition methods.