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arXiv · 2211.01544

Pathology of submeasures and $F_σ$ ideals

Jorge Martínez·David Meza-Alcántara·Carlos Uzcátegui
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Abstract

We address some phenomena about the interaction between lower semicontinuous submeasures on $\mathbb{N}$ and $F_σ$ ideals. We analyze the pathology degree of a submeasure and present a method to construct pathological $F_σ$ ideals. We give a partial answers to the question of whether every nonpathological tall $F_σ$ ideal is Katětov above the random ideal or at least has a Borel selector. Finally, we show a representation of nonpathological $F_σ$ ideals using sequences in Banach spaces.

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Jorge Martínez, David Meza-Alcántara, Carlos Uzcátegui. 2024-04-22. Pathology of submeasures and $F_σ$ ideals. https://arxiv.org/abs/2211.01544

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