论文标题
黄金之王关于无效套装的原则
Goldstern's principle about unions of null sets
论文作者
论文摘要
金斯特恩（Goldstern）在1993年的论文中表明，勒布斯格（Lebesgue）衡量零套件的一个真实参数单调家族的结合也使勒布斯格（Lebesgue）衡量零，前提是这些集合均匀地是$ \boldsymbolς^1_1 $。我们的目的是研究在多大程度上可以放弃$ \boldsymbolς^1_1 $假设。我们展示了Goldstern的PointClass $ \BOLDSYMBOLπ^1_1 $保留的原则。我们表明，黄金人的所有子集的点级原理与$ \ mathsf {zfc} $一致，并从$ \ mathsf {ch} $中表示其否定。另外，我们证明，黄金人的所有子集的点级原理都在$ \ mathsf {zf} + \ mathsf {ad} $和solovay模型下均持有。
Goldstern showed in his 1993 paper that the union of a real-parametrized, monotone family of Lebesgue measure zero sets has also Lebesgue measure zero provided that the sets are uniformly $\boldsymbolΣ^1_1$. Our aim is to study to what extent we can drop the $\boldsymbolΣ^1_1$ assumption. We show Goldstern's principle for the pointclass $\boldsymbolΠ^1_1$ holds. We show that Goldstern's principle for the pointclass of all subsets is consistent with $\mathsf{ZFC}$ and show its negation follows from $\mathsf{CH}$. Also we prove that Goldstern's principle for the pointclass of all subsets holds both under $\mathsf{ZF} + \mathsf{AD}$ and in Solovay models.
