Journal of the Mathematical Society of Japan

Stationary reflection and the club filter

Masahiro SHIOYA

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Abstract

Suppose that κ is a regular uncountable cardinal. It has been known that the club filter on P ω 1 κ can be presaturated. In this paper we extend the result to the case of P μ κ , where μ is a regular uncountable cardinal κ . This involves suitably weakening the notion of presaturation. A new reflection principle for stationary sets in P κ λ 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

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1197320627

Digital Object Identifier
doi:10.2969/jmsj/05941045

Mathematical Reviews number (MathSciNet)
MR2370005

Zentralblatt MATH identifier
1270.03082

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

Keywords
large cardinal forcing presaturation

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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