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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2508.15362 |
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| _version_ | 1866908497085464576 |
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| author | Johnson, Will |
| author_facet | Johnson, Will |
| contents | Let $K$ be a countable field. Then $K$ is large in the sense of Pop if and only if it admits a field topology which is "generalized t-henselian" (gt-henselian) in the sense of Dittmann, Walsberg, and Ye, meaning that the implicit function theorem holds for polynomials. Moreover, the étale open topology can be characterized in terms of the gt-henselian topologies on $K$: a subset $U \subseteq K^n$ is open in the étale open topology if and only if it is open with respect to every gt-henselian topology on $K$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_15362 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Largeness and generalized t-henselianity Johnson, Will Logic Commutative Algebra 12J99, 12E30, 12L12 Let $K$ be a countable field. Then $K$ is large in the sense of Pop if and only if it admits a field topology which is "generalized t-henselian" (gt-henselian) in the sense of Dittmann, Walsberg, and Ye, meaning that the implicit function theorem holds for polynomials. Moreover, the étale open topology can be characterized in terms of the gt-henselian topologies on $K$: a subset $U \subseteq K^n$ is open in the étale open topology if and only if it is open with respect to every gt-henselian topology on $K$. |
| title | Largeness and generalized t-henselianity |
| topic | Logic Commutative Algebra 12J99, 12E30, 12L12 |
| url | https://arxiv.org/abs/2508.15362 |