论文标题
kuratowski闭合填充变体，其解决方案与ZF无关
A Kuratowski closure-complement variant whose solution is independent of ZF
论文作者
论文摘要
我们提出了Kuratowski封闭汇编问题的以下新变体：通过从一套$ a $ a $ a $ a波兰空间$ x $开始获得多少个不同的集合，并仅按照订单进行封闭，补充和$ d $运算符，并经常按需要？ Kuratowski在他的基本文本\ textit {topology：卷I}中研究了套装运算符$ d $;它分配了$ a $ $ a $的所有点的$ a $ collection $ da $。我们表明，在ZFC集理论中，此变体问题的答案是$ 22 $。在与ZFC（即ZF+DC+pb）的独特系统中，答案仅为$ 18 $。
We pose the following new variant of the Kuratowski closure-complement problem: How many distinct sets may be obtained by starting with a set $A$ of a Polish space $X$, and applying only closure, complementation, and the $d$ operator, as often as desired, in any order? The set operator $d$ was studied by Kuratowski in his foundational text \textit{Topology: Volume I}; it assigns to $A$ the collection $dA$ of all points of second category for $A$. We show that in ZFC set theory, the answer to this variant problem is $22$. In a distinct system equiconsistent with ZFC, namely ZF+DC+PB, the answer is only $18$.
