A note on existentially t-henselian fields
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866918422871277568 |
|---|---|
| author | Anscombe, Sylvy |
| author_facet | Anscombe, Sylvy |
| contents | A field is existentially t-henselian if it is has the same existential theory in the first-order language of rings as a field that admits a nontrivial henselian valuation. This property turns out to be equivalent to $\mathbb{Z}$-largeness, which is a property identified in previous work with Fehm, and which holds for $F$ if and only if $tF[\![t]\!]$ is not Diophantine in $F(\!(t)\!)$, without extra constants. In this short note, we further investigate this property in order to count the number of existential theories of henselian valuations on a given field, and to find other characterizations of existential t-henselianity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_27612 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A note on existentially t-henselian fields Anscombe, Sylvy Logic 03C60, 12J20 A field is existentially t-henselian if it is has the same existential theory in the first-order language of rings as a field that admits a nontrivial henselian valuation. This property turns out to be equivalent to $\mathbb{Z}$-largeness, which is a property identified in previous work with Fehm, and which holds for $F$ if and only if $tF[\![t]\!]$ is not Diophantine in $F(\!(t)\!)$, without extra constants. In this short note, we further investigate this property in order to count the number of existential theories of henselian valuations on a given field, and to find other characterizations of existential t-henselianity. |
| title | A note on existentially t-henselian fields |
| topic | Logic 03C60, 12J20 |
| url | https://arxiv.org/abs/2603.27612 |