Stationary reflection and the club filter

Abstract

Suppose that κ is a regular uncountable cardinal. It has been known that the club filter on \\mathcal{P}_ω1κ can be presaturated. In this paper we extend the result to the case of \\mathcal{P}_μκ, where μ is a regular uncountable cardinal ≤κ. This involves suitably weakening the notion of presaturation. A new reflection principle for stationary sets in \\mathcal{P}_κλ plays a key role.