Weakly normal ideals ou PKl and the singular cardinal hypothesis

Yoshihiro Abe

ArticleOriginal scientific text

Title

Weakly normal ideals ou PKl and the singular cardinal hypothesis

Authors ^1,²

Affiliations

Numazu College of Technology, 3600 Ooka, Numazu-Shi, Shizuoka, 410 Japan
Department of Mathematics, Kanagawa University, Rokkakubashi, Kanagawa-Ku, Yokohama 221, Japan

Abstract

In §1, we observe that a weakly normal ideal has a saturation property; we also show that the existence of certain precipitous ideals is sufficient for the existence of weakly normal ideals. In §2, generalizing Solovay's theorem concerning strongly compact cardinals, we show that

λ^{< κ}

is decided if

P_{κ} λ

carries a weakly normal ideal and λ is regular or cf λ ≤ κ. This is applied to solving the singular cardinal hypothesis.

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Additional information

http://matwbn.icm.edu.pl/ksiazki/fm/fm143/fm14321.pdf

Title

Weakly normal ideals ou PKl and the singular cardinal hypothesis

Affiliations

Abstract

Bibliography

Additional information