PreprintCC BY 4.0arXiv
The Higher Closed Null Ideal(s)
Abstract
We generalise the σ-ideal 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 characteristics of the higher closed null ideals and other cardinal characteristics.
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BibTeX
@misc{marton2026higher,
title = {{The Higher Closed Null Ideal(s)}},
author = {Adam Marton and Jaroslav Šupina and Miroslav Repický and Tristan van der Vlugt},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05784},
eprint = {2610.05784},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05784},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Higher Closed Null Ideal(s)
AU - Adam Marton
AU - Jaroslav Šupina
AU - Miroslav Repický
AU - Tristan van der Vlugt
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.05784
UR - https://arxiv.org/abs/2610.05784
AB - We generalise the σ-ideal 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 characteristics of the higher closed null ideals and other cardinal characteristics.
ER -