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arXiv · 2610.05784

The Higher Closed Null Ideal(s)

Adam Marton·Jaroslav Šupina·Miroslav Repický·Tristan van der Vlugt
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Abstract

We generalise the $σ$-ideal $\mathcal E$ generated by the closed Lebesgue null subsets of the Cantor space ${}^ω2$ to the context of higher Cantor spaces ${}^κ2$ for an uncountable cardinal $κ$ satisfying $κ=κ^{<κ}$. We introduce candidates for a higher closed null ideal based on slaloms on partitions of $κ$ into sets of size ${<}κ$, and study their combinatorial properties. We also give some relations between the cardinal invariants of the higher closed null ideals and other cardinal characteristics.

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Adam Marton, Jaroslav Šupina, Miroslav Repický, Tristan van der Vlugt. 2026-10-05. The Higher Closed Null Ideal(s). https://arxiv.org/abs/2610.05784

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