Quasi-Polish spaces and spaces of filters in second-order arithmetic
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866910222213185536 |
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| author | Kaneko, Yuzuki Yokoyama, Keita |
| author_facet | Kaneko, Yuzuki Yokoyama, Keita |
| contents | The class of quasi-Polish spaces admits several equivalent representations, including UF spaces, NP spaces, $\mathbfΠ_2^0$ subspaces of $\mathcal{P}(\mathbb{N})$, and sober spaces of countably presented frames. In this paper, we formalize these structures within second-order arithmetic and conduct a systematic reverse mathematical analysis of the transitions between them. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_15052 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quasi-Polish spaces and spaces of filters in second-order arithmetic Kaneko, Yuzuki Yokoyama, Keita Logic The class of quasi-Polish spaces admits several equivalent representations, including UF spaces, NP spaces, $\mathbfΠ_2^0$ subspaces of $\mathcal{P}(\mathbb{N})$, and sober spaces of countably presented frames. In this paper, we formalize these structures within second-order arithmetic and conduct a systematic reverse mathematical analysis of the transitions between them. |
| title | Quasi-Polish spaces and spaces of filters in second-order arithmetic |
| topic | Logic |
| url | https://arxiv.org/abs/2605.15052 |