Stationary reflection and the club filter

Abstract

Suppose that $\kappa$ is a regular uncountable cardinal. It has been known that the club filter on ${\mathit{P}}_{{\omega }_1}\kappa$ can be presaturated. In this paper we extend the result to the case of ${\mathit{P}}_{\mu }\kappa$, where $\mu$ is a regular uncountable cardinal $\le \kappa$. This involves suitably weakening the notion of presaturation. A new reflection principle for stationary sets in ${\mathit{P}}_{\kappa }\lambda$ plays a key role.