论文标题
Baire空间，可衡量的红衣主教和陡峭理想的Kuratowski分区之间的连接
Connections between Kuratowski partitions of Baire spaces, measurable cardinals and precipitous ideals
论文作者
论文摘要
在本文中，我们介绍了一些$ k $ - 分区的属性，这些属性是baire空间的分区，使得该分区的所有亚家族汇总到带有Baire属性的集合。在结果证明的一般存在中，我们已经表明，任何$ k $ - 分区的存在意味着存在于$ k $ - 分区的可分离空间以及$ k $ - 紧凑型空间的存在意味着存在$ k $的存在。我们还证明了$ k $ - 分区的存在与存在艰巨的理想以及可衡量的红衣主教之间的某些联系。还概述了可能与可实现的红衣主教，封闭间隔和密度拓扑的Lebesgue度量的扩展。
In this paper we present a few properties of $K$-partitions, which are partitions of Baire spaces such that all subfamilies of such a partition sum to a set with the Baire property. Among the result proven we have general existence result that state that the existence of any $K$-partition implies the existence of $K$-partition of a metrizable space as well as existence of $K$-partition of a compact space implies the existence of $K$-partition of a completely metrizable space. We also prove some connections between existence of $K$-partitions and existence of precipitous ideals as well as measurable cardinals. There are also outlined possible connection with real-measurable cardinals, extensions of Lebesgue measure on the closed interval and density topologies.
