Cardinal invariants associated with Hausdorff measures

IF 0.5 4区数学 Q1 Arts and Humanities

Archive for Mathematical Logic Pub Date : 2025-03-17 DOI:10.1007/s00153-025-00970-9

Tatsuya Goto

引用次数: 0

Abstract

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 \(0< s < 1\) and of the Lebesgue null ideal can be separated using the Mathias forcing.

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与豪斯多夫测度相关的基数不变量

我们考虑由豪斯多夫测度决定的基数不变量。我们使用两个模型分离了Hausdorff测度0理想的许多基数不变量，这两个模型同时从早期的工作中分离了Yorioka理想的许多基数不变量。此外，我们还证明了s维Hausdorff测度0理想（\(0< s < 1\)）和Lebesgue零理想（Lebesgue零理想）的均匀性数可以用Mathias强迫分离。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Archive for Mathematical Logic MATHEMATICS-LOGIC

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The journal publishes research papers and occasionally surveys or expositions on mathematical logic. Contributions are also welcomed from other related areas, such as theoretical computer science or philosophy, as long as the methods of mathematical logic play a significant role. The journal therefore addresses logicians and mathematicians, computer scientists, and philosophers who are interested in the applications of mathematical logic in their own field, as well as its interactions with other areas of research.