关于完全空集类及其传递形式
On the class of perfectly null sets and its transitive version
摘要：
本文引入了两类新的实数直线的特殊子集：完全空集类和传递意义下完全空集类。这些类可以在类别侧上对相应的类起替代作用。我们研究了它们的性质，特别是证明了每个强零集在传递意义下是完全零的，并且证明了存在一个在传递意义下不是完全零的泛零集与ZFC是一致的.最后，我们陈述了关于上述类的一些开放性问题。虽然完全空集和泛空集的类是否一致不同的主要问题仍然是开放的，我们证明了与这个问题有关的一些结果。
英文摘要：
We introduce two new classes of special subsets of the real line: the class of perfectly null sets and the class of sets which are perfectly null in the transitive sense. These classes may play the role of duals to the corresponding classes on the category side. We investigate their properties and, in particular, we prove that every strongly null set is perfectly null in the transitive sense, and that it is consistent with ZFC that there exists a universally null set which is not perfectly null in the transitive sense. Finally, we state some open questions concerning the above classes. Although the main problem of whether the classes of perfectly null sets and universally null sets are consistently different remains open, we prove some results related to this question.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
