Connections between Kuratowski partitions of Baire spaces, measurable cardinals and precipitous ideals

2022/05/25 by Sławomir Kusiński, Kusiński, Sławomir
Mathematics · #03E99 #28E15 #54A99 #Advanced Topology and Set Theory #FOS: Mathematics #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.2205.12653

openalex publication_date 2022/05/25 · openalex created_date 2022/06/13 · openalex updated_date 2026/07/28

Abstract

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.

Related

• Some remarks on Kuratowski partitions
• Partitions of non-complete Baire metric spaces
• On Kuratowski partitions
• Partitions and point-finite covers of Baire spaces
• Equivalence of the existence of K-partitions with the existence of the precipitous ideal