Weakly normal ideals ou PKl and the singular cardinal hypothesis

Volume 143 / 1993

Yoshihiro Abe Fundamenta Mathematicae 143 (1993), 97-106 DOI: 10.4064/fm-143-2-97-106


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


  • Yoshihiro Abe

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