Growing Spines Ad Infinitum
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915231052070912 |
|---|---|
| author | Boissonneau, Blaise De Mase, Anna Jahnke, Franziska Touchard, Pierre |
| author_facet | Boissonneau, Blaise De Mase, Anna Jahnke, Franziska Touchard, Pierre |
| contents | We show that every non-trivial ordered abelian group $G$ is augmentable by infinite elements, i.e., we have $G\preccurlyeq H\oplus G$ for some non-trivial ordered abelian group $H$. As an application, we show that when $k$ is a field of characteristic 0, then $k$ is not $t$-henselian if and only if all henselian valuations with residue field $k$ are ($\emptyset$-)definable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_10531 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Growing Spines Ad Infinitum Boissonneau, Blaise De Mase, Anna Jahnke, Franziska Touchard, Pierre Logic Group Theory 03C60, 03C64, 06F20 (Primary), 12J20, 12L12 (Secondary) We show that every non-trivial ordered abelian group $G$ is augmentable by infinite elements, i.e., we have $G\preccurlyeq H\oplus G$ for some non-trivial ordered abelian group $H$. As an application, we show that when $k$ is a field of characteristic 0, then $k$ is not $t$-henselian if and only if all henselian valuations with residue field $k$ are ($\emptyset$-)definable. |
| title | Growing Spines Ad Infinitum |
| topic | Logic Group Theory 03C60, 03C64, 06F20 (Primary), 12J20, 12L12 (Secondary) |
| url | https://arxiv.org/abs/2501.10531 |