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\(c\)-Luzin sets, nonatomic \(\sigma\)-fields and \(\sigma\)-independent sets. (English) Zbl 1163.03028
Summary: It is proved that if \(L\) is a \(\mathfrak c\)-Luzin set then, assuming MA + negation of CH, the \(\sigma\)-field \({\mathcal B}_L\) of Borel subsets of \(L\) contains a nonatomic \(\sigma\)-field separating points. Other properties of \({\mathcal B}_L\) are also considered.
MSC:
03E15 Descriptive set theory
03E50 Continuum hypothesis and Martin’s axiom
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