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arXiv · 2205.12653

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

Sławomir Kusiński
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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.

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Sławomir Kusiński. 2022-05-25. Connections between Kuratowski partitions of Baire spaces, measurable cardinals and precipitous ideals. https://arxiv.org/abs/2205.12653

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