On a conjecture of Debs and Saint Raymond
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2021
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| _version_ | 1866910770631016448 |
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| author | Kwela, Adam |
| author_facet | Kwela, Adam |
| contents | Borel separation rank of an analytic ideal $\mathcal{I}$ on $ω$ is the minimal ordinal $α<ω_{1}$ such that there is $\mathcal{S}\in\bf{Σ^0_{1+α}}$ with $\mathcal{I}\subseteq \mathcal{S}$ and $\mathcal{I}^\star\cap \mathcal{S}=\emptyset$, where $\mathcal{I}^\star$ is the filter dual to the ideal $\mathcal{I}$. Answering in negative a question of G. Debs and J. Saint Raymond [Fund. Math. 204 (2009), no. 3], we construct a Borel ideal of rank $>2$ which does not contain an isomorphic copy of the ideal $\text{Fin}^3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_01516 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On a conjecture of Debs and Saint Raymond Kwela, Adam Logic Borel separation rank of an analytic ideal $\mathcal{I}$ on $ω$ is the minimal ordinal $α<ω_{1}$ such that there is $\mathcal{S}\in\bf{Σ^0_{1+α}}$ with $\mathcal{I}\subseteq \mathcal{S}$ and $\mathcal{I}^\star\cap \mathcal{S}=\emptyset$, where $\mathcal{I}^\star$ is the filter dual to the ideal $\mathcal{I}$. Answering in negative a question of G. Debs and J. Saint Raymond [Fund. Math. 204 (2009), no. 3], we construct a Borel ideal of rank $>2$ which does not contain an isomorphic copy of the ideal $\text{Fin}^3$. |
| title | On a conjecture of Debs and Saint Raymond |
| topic | Logic |
| url | https://arxiv.org/abs/2109.01516 |