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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:
 3e+15 Descriptive set theory 3e+50 Continuum hypothesis and Martin’s axiom
##### Keywords:
Borel set; Martin’s Axiom; Luzin set
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