Cichoń's maximum with cardinals of the closed null ideal
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909667646504960 |
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| author | Yamazoe, Takashi |
| author_facet | Yamazoe, Takashi |
| contents | Let $\mathcal{E}$ denote the $σ$-ideal generated by closed null sets on the reals. We show that the uniformity and the covering of $\mathcal{E}$ can be added to Cichoń's maximum with distinct values. More specifically, it is consistent that $\aleph_1<\mathrm{add}(\mathcal{N})<\mathrm{cov}(\mathcal{N})<\mathfrak{b}<\mathrm{non}(\mathcal{E})<\mathrm{non}(\mathcal{M})<\mathrm{cov}(\mathcal{M})<\mathrm{cov}(\mathcal{E})<\mathfrak{d}<\mathrm{non}(\mathcal{N})<\mathrm{cof}(\mathcal{N})<2^{\aleph_0}$ holds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_09069 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cichoń's maximum with cardinals of the closed null ideal Yamazoe, Takashi Logic 03E17, 03E35 Let $\mathcal{E}$ denote the $σ$-ideal generated by closed null sets on the reals. We show that the uniformity and the covering of $\mathcal{E}$ can be added to Cichoń's maximum with distinct values. More specifically, it is consistent that $\aleph_1<\mathrm{add}(\mathcal{N})<\mathrm{cov}(\mathcal{N})<\mathfrak{b}<\mathrm{non}(\mathcal{E})<\mathrm{non}(\mathcal{M})<\mathrm{cov}(\mathcal{M})<\mathrm{cov}(\mathcal{E})<\mathfrak{d}<\mathrm{non}(\mathcal{N})<\mathrm{cof}(\mathcal{N})<2^{\aleph_0}$ holds. |
| title | Cichoń's maximum with cardinals of the closed null ideal |
| topic | Logic 03E17, 03E35 |
| url | https://arxiv.org/abs/2412.09069 |