## Journal of the Mathematical Society of Japan

### Stationary reflection and the club filter

Masahiro SHIOYA

#### Abstract

Suppose that $\kappa$ is a regular uncountable cardinal. It has been known that the club filter on $\mathcal{P}_{\omega_1}\kappa$ can be presaturated. In this paper we extend the result to the case of $\mathcal{P}_{\mu}\kappa$, 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 $\mathcal{P}_{\kappa}\lambda$ plays a key role.

#### Article information

Source
J. Math. Soc. Japan, Volume 59, Number 4 (2007), 1045-1065.

Dates
First available in Project Euclid: 10 December 2007

https://projecteuclid.org/euclid.jmsj/1197320627

Digital Object Identifier
doi:10.2969/jmsj/05941045

Mathematical Reviews number (MathSciNet)
MR2370005

Zentralblatt MATH identifier
1270.03082

#### Citation

SHIOYA, Masahiro. Stationary reflection and the club filter. J. Math. Soc. Japan 59 (2007), no. 4, 1045--1065. doi:10.2969/jmsj/05941045. https://projecteuclid.org/euclid.jmsj/1197320627

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