The Category Dichotomy for Ideals
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918276977655808 |
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| author | Dow, Alan Figueroa-Sierra, Raul Guzmán, Osvaldo Hrušák, Michael |
| author_facet | Dow, Alan Figueroa-Sierra, Raul Guzmán, Osvaldo Hrušák, Michael |
| contents | We provide a counterexample to the Category Dichotomy in the framework of $\textsf{ZFC}$. That is, we prove the existence of an ideal on $ω$ that is not Katětov below $\mathsf{nwd}$ and does not have restrictions above $\mathcal{ED}$. We also prove that in the Laver model every tall $\mathsf{P}$-ideal is Katětov-Blass above $\mathcal{ED}_{\mathsf{fin}}$ and that it is consistent that every $\mathsf{Q}^{+}$ ideal is meager. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_02290 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Category Dichotomy for Ideals Dow, Alan Figueroa-Sierra, Raul Guzmán, Osvaldo Hrušák, Michael Logic 03E05, 03E17, 03E75 F.4.1 We provide a counterexample to the Category Dichotomy in the framework of $\textsf{ZFC}$. That is, we prove the existence of an ideal on $ω$ that is not Katětov below $\mathsf{nwd}$ and does not have restrictions above $\mathcal{ED}$. We also prove that in the Laver model every tall $\mathsf{P}$-ideal is Katětov-Blass above $\mathcal{ED}_{\mathsf{fin}}$ and that it is consistent that every $\mathsf{Q}^{+}$ ideal is meager. |
| title | The Category Dichotomy for Ideals |
| topic | Logic 03E05, 03E17, 03E75 F.4.1 |
| url | https://arxiv.org/abs/2503.02290 |