Measurable cardinals and the continuum hypothesis

Measurable cardinals and the continuum hypothesis
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可测基数和连续统假设

DOI：
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发表时间：
1967
期刊：
影响因子：
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通讯作者：
R. M. Solovay
R. M. Solovay
中科院分区：
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文献类型：
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作者：
Azriel Levy;R. M. Solovay

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设Zfm是集合论ZF和一个公理，该公理断言存在一个可测基数。证明了如果ZFM是相容的，则ZFM与每一句φ相容，而每一句ZFM的相合性是用科恩的强迫法和一组基数&k条件来证明的，特别是如果ZFM相容，则它与连续统假设及其否定是一致的。
Let ZFM be the set theory ZF together with an axiom which asserts the existence of a measurable cardinal. It is shown that if ZFM is consistent then ZFM is consistent with every sentence φ whose consistency is proved by Cohen’s forcing method with a set of conditions of cardinality <k. In particular, if ZFM is consistent then it is consistent with the continuum hypothesis and with its negation.