Open Access
January, 2002 Partition properties on Pκλ
Shizuo KAMO
J. Math. Soc. Japan 54(1): 123-133 (January, 2002). DOI: 10.2969/jmsj/1191593957


Menas [13] showed there exist 22λ<κ normal ultrafilters on Pκλ with the partition property if κ is 2λ<κ-supercompact. We first show that λ-supercompactness of κ implies the existence of a normal ultrafilter on Pκλ with the partition property. We also prove by a similar technic that part*(κ,λ) holds if κ is λ-ineffable with cf(λ)κ. Note that Magidor [11] showed κ is λ-ineffable if part*(κ,λ) holds, and we proved the converse under some additional assumption in [7].


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Shizuo KAMO. "Partition properties on Pκλ." J. Math. Soc. Japan 54 (1) 123 - 133, January, 2002.


Published: January, 2002
First available in Project Euclid: 5 October 2007

zbMATH: 1027.03036
MathSciNet: MR1864930
Digital Object Identifier: 10.2969/jmsj/1191593957

Primary: 03E55
Secondary: 04A20

Keywords: normal ultrafilter , partition property , supercompactness

Rights: Copyright © 2002 Mathematical Society of Japan

Vol.54 • No. 1 • January, 2002
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