Goldstern's Principle with respect to Hausdorff Measures
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866908818921750528 |
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| author | Goto, Tatsuya |
| author_facet | Goto, Tatsuya |
| contents | This paper is a continuation of the paper [Got25] and studies Goldstern's principle, a principle about unions of continuum many null sets, further. The main result is that the Hausdorff measure version of Goldstern's principle for $\boldsymbolΠ^1_1$ sets fails in $L$, despite the fact that the Lebesgue measure version is true. Moreover, we show that this version holds provided that the measurable cardinal exists. Other various results regarding Goldstern's principle are established. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_22852 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Goldstern's Principle with respect to Hausdorff Measures Goto, Tatsuya Logic 03E15 This paper is a continuation of the paper [Got25] and studies Goldstern's principle, a principle about unions of continuum many null sets, further. The main result is that the Hausdorff measure version of Goldstern's principle for $\boldsymbolΠ^1_1$ sets fails in $L$, despite the fact that the Lebesgue measure version is true. Moreover, we show that this version holds provided that the measurable cardinal exists. Other various results regarding Goldstern's principle are established. |
| title | Goldstern's Principle with respect to Hausdorff Measures |
| topic | Logic 03E15 |
| url | https://arxiv.org/abs/2512.22852 |