Partition properties on

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概要

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• Menas [{13}] showed there exist 2^{2^{λ<SUP><κ</SUP>}} normal ultrafilters on \mathscr{P}<SUB>κ</SUB>λ with the partition property if κ is 2^{λ<SUP><κ</SUP>}-supercompact. We first show that λ-supercompactness of κ implies the existence of a normal ultrafilter on \mathscr{P}<SUB>κ</SUB>λ with the partition property. We also prove by a similar technic that part<SUP>*</SUP>(κ, λ) holds if κ is λ-ineffable with cf(λ)≥qκ. Note that Magidor [{11}] showed κ is λ-ineffable if part<SUP>*</SUP>(κ, λ) holds, and we proved the converse under some additional assumption in [7].

• 社団法人 日本数学会の論文

著者

• Kamo Shizuo

  University Of Osaka Prefecture

関連論文

• Partition properties on

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