More on real-valued measurable cardinals and forcing with ideals
More on real-valued measurable cardinals and forcing with ideals
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更多关于实值可测量基数和理想强迫的内容
DOI：
10.1007/bf02772619
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发表时间：
1995
影响因子：
1
通讯作者：
S. Shelah
中科院分区：
文献类型：
--
作者：
M. Gitik;S. Shelah
（1）证明了若f_c是实值可测的，则（c，P（c），σ）的Maharam型为2c。这回答了D的一个问题。Fremlin [Fr，（P2f）]. (2)给出了一个与R不同的具有实值可测基数的模型的构造。Solovay [So].这回答了D的一个问题。Fremlin [Fr，（P1）]. (3)集合X上κ-完全理想的强迫，|X| ≥κ不能同构于随机×科恩或科恩×随机。X =κ的结果在[Gi-Sh 1]中已被证明，但正如M. Burke，它在[Gi-Sh 2]中的应用需要处理任何X。应用程序是：如果An是一组实数，当n <ω时，则对于某个两两不相交的Bn（当n <ω时），我们有Bn ∈ An，但它们有相同的外勒贝格测度。
Abstract(1) It is shown that ifc is real-valued measurable then the Maharam type of (c, P(c),σ) is 2c. This answers a question of D. Fremlin [Fr, (P2f)].(2) A different construction of a model with a real-valued measurable cardinal is given from that of R. Solovay [So]. This answers a question of D. Fremlin [Fr, (P1)].(3) The forcing with aκ-complete ideal over a setX, |X| ≥κ cannot be isomorphic to Random × Cohen or Cohen × Random. The result forX=κ was proved in [Gi-Sh1] but, as was pointed out to us by M. Burke, the application of it in [Gi-Sh2] requires dealing with anyX. The application is: ifAn is a set of reals forn<ω then for some pairwise disjointBn (forn<ω) we haveBn ⊆An but they have the same outer Lebesgue measure.