Stationary reflection and the club filter. (English) Zbl 1270.03082

Shioya, Masahiro

J. Math. Soc. Japan 59, No. 4, 1045-1065 (2007).

Summary: Suppose that \(\kappa\) is a regular uncountable cardinal. It has been known that the club filter on \(P_{\omega_1}\kappa\) can be presaturated. In this paper we extend the result to the case of \(P_{\mu}\kappa\), where \(\mu\) is a regular uncountable cardinal \(\leq\kappa\). This involves suitably weakening the notion of presaturation. A new reflection principle for stationary sets in \(P_{\kappa}\lambda\) plays a key role.

MSC:

03E05	Other combinatorial set theory
03E35	Consistency and independence results
03E55	Large cardinals

Keywords:

large cardinal; forcing; presaturation