完全贫乏集与泛空集

在完全贫乏的集合上

On perfectly meager sets

一组真正的A被称为完全贫乏，如果一个\cap P是贫乏的P，对每一个完满集P. Marczewski问，如果产品的完全贫乏集是完全贫乏。在文件中，它表明，这是一致的，这个问题的答案是肯定的。(It已知答案是否定的也是一致的（Reclaw））

Countably perfectly meager sets

We study a strengthening of the notion of a perfectly meager set. We say that that a subset $A$ of a perfect Polish space $X$ is countably perfectly meager in $X$, if for every sequence of perfect subsets $\{P_n: n \in {\mathbb N}\}$ of $X$, there exists an $F_σ$-set $F$ in $X$ such that $A \subseteq F$ and $F\cap P_n$ is meager in $P_n$ for each $n$. We give various characterizations and examples of countably perfectly meager sets. We prove that not every universally meager set is countably perfectly meager correcting an earlier result of Bartoszyński.

可数完全贫乏集与可数完全零集

Countably perfectly meager and countably perfectly null sets

本文通过引入可数完全贫乏集和可数完全零集以强化普遍贫乏集与普遍零集概念，并在连续统假设弱化条件下证明了二者不等价。

在Miller模型及其他模型中的普遍渺小集

Universally meager sets in the Miller model and similar ones

研究在Miller模型及其他模型中普遍渺小集的大小限制，证明强测度零集的大小至多为ω₁，并探讨相关覆盖性质与空间结构的关系。

关于小实数集的注记

Remarks on small sets of reals

证明了对偶Borel猜想蕴涵${\mathfrak d}> \aleph_1$，并给出了完全贫乏集和泛贫乏集的一些拓扑刻画.

On the class of perfectly null sets and its transitive version

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. Althoug…