Cardinal invariants associated with Hausdorff measures

2021/12/15 by Tatsuya Goto, Goto, Tatsuya · 1 citation
Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.2112.07952

openalex publication_date 2021/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider cardinal invariants determined from Hausdorff measures. We separate many cardinal invariants of Hausdorff measure 0 ideals using two models that separate many cardinal invariants of Yorioka ideals at once from earlier work. Also we show the uniformity numbers of s-dimensional Hausdorff measure 0 ideals for 0 < s < 1 and that of Lebesgue null ideal can be separated using the Mathias forcing.

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• Separating covering numbers and separating uniformity numbers of Hausdorff measures need large continuum

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