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arXiv · 2405.11312

Cardinal characteristics associated with small subsets of reals

Miguel A. Cardona·Adam Marton·Jaroslav Supina
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Abstract

Inspired by Bartoszyński's work on small sets, we introduce a new ideal defined by interval partitions on natural numbers and summable sequences of positive reals. Similarly, we present another ideal that relies on Bartoszyński's and Shelah's representation of $F_σ$ measure zero sets. We show they are $σ$-ideals characterizing all small sets and $F_σ$ measure zero sets. We also study the cardinal characteristics associated with the introduced ideals. We use them to describe the invariants of measure, discuss their connection to Cichoń's diagram, and present related consistency results.

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Miguel A. Cardona, Adam Marton, Jaroslav Supina. 2025-02-12. Cardinal characteristics associated with small subsets of reals. https://arxiv.org/abs/2405.11312

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