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An ultrafilter with property $ \sigma$

Author: Masahiro Shioya
Journal: Proc. Amer. Math. Soc. 134 (2006), 1819-1821
MSC (2000): Primary 03E05, 03E55
Published electronically: October 28, 2005
MathSciNet review: 2207498
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Abstract: Let $ \kappa$ be a $ \lambda$-supercompact cardinal. We show that $ \mathcal{P}_\kappa\lambda$ carries a normal ultrafilter with a property introduced by Menas. With it we give a transparent proof of Kamo's theorem that $ \mathcal{P}_\kappa\lambda$ carries a normal ultrafilter with the partition property.

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Additional Information

Masahiro Shioya
Affiliation: Institute of Mathematics, University of Tsukuba, Tsukuba, 305-8571 Japan

Keywords: $\mathcal{P}_\kappa\lambda$, property $\sigma$, partition property
Received by editor(s): April 1, 2004
Received by editor(s) in revised form: December 30, 2004
Published electronically: October 28, 2005
Additional Notes: This work was partially supported by JSPS Grant-in-Aid No. 16540094.
Communicated by: Carl G. Jockusch, Jr.
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.