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<p>We consider cardinal invariants determined by 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 <i>s</i>-dimensional Hausdorff measure 0 ideals for <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="153_2025_970_Article_IEq1.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="71" /> </InlineMediaObject> <EquationSource Format="TEX">\(0&lt; s &lt; 1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>0</mn> <mo>&lt;</mo> <mi>s</mi> <mo>&lt;</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> and of the Lebesgue null ideal can be separated using the Mathias forcing.</p>

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Cardinal invariants associated with Hausdorff measures

  • 期刊论文

  • 发表日期：

    2025年3月17日

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  • Tatsuya Goto

摘要

We consider cardinal invariants determined by 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 \(0< s < 1\) 0 < s < 1 and of the Lebesgue null ideal can be separated using the Mathias forcing.