Large cardinals with few measures
Large cardinals with few measures
复制标题
大基数，措施少
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
J. Hamkins
中科院分区：
文献类型：
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作者：
Arthur W. Apter;J. Cummings;J. Hamkins
我们证明，假设一个可测基数的一致性，在最小可测基数k上有恰好k +个正规度量是一致的。这回答了Stewart Baldwin的一个问题。该方法推广到更高的基数上，表明如果λ > K是正则基数，则P κ (λ)上的A强紧性或A超紧性测度的个数可以恰好为λ +。最后，我们列出一系列悬而未决的问题。我们的证明使用了詹姆斯·卡明斯的一个重要观察。
We show, assuming the consistency of one measurable cardinal, that it is consistent for there to be exactly κ + many normal measures on the least measurable cardinal K. This answers a question of Stewart Baldwin. The methods generalize to higher cardinals, showing that the number of A strong compactness or A supercompactness measures on P κ (λ) can be exactly λ + if λ > K is a regular cardinal. We conclude with a list of open questions. Our proofs use a critical observation due to James Cummings.