Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.06986 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915991028498432 |
|---|---|
| author | Johnson, Will |
| author_facet | Johnson, Will |
| contents | Let $T$ be a theory which is t-minimal, meaning that with respect to some definable topology, a unary definable set $D \subseteq M$ has non-empty interior iff it is infinite. If $K$ is a definable field in $T$, then $K$ is finite or "large" in the sense of Pop: any smooth algebraic curve $C$ over $K$ with at least one $K$-rational point has infinitely many $K$-rational points. We also assign a canonical topology to any abelian definable group $G$ in a t-minimal theory. In the case where the t-minimal theory is "visceral" in the sense of Dolich and Goodrick, meaning that the definable topology is induced by a definable uniformity, we can drop the assumption of abelianity of $G$, and the resulting topology on $G$ is a definable manifold in the style of Acosta López and Hasson. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_06986 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Definable groups and fields in t-minimal theories Johnson, Will Logic 03C60 Let $T$ be a theory which is t-minimal, meaning that with respect to some definable topology, a unary definable set $D \subseteq M$ has non-empty interior iff it is infinite. If $K$ is a definable field in $T$, then $K$ is finite or "large" in the sense of Pop: any smooth algebraic curve $C$ over $K$ with at least one $K$-rational point has infinitely many $K$-rational points. We also assign a canonical topology to any abelian definable group $G$ in a t-minimal theory. In the case where the t-minimal theory is "visceral" in the sense of Dolich and Goodrick, meaning that the definable topology is induced by a definable uniformity, we can drop the assumption of abelianity of $G$, and the resulting topology on $G$ is a definable manifold in the style of Acosta López and Hasson. |
| title | Definable groups and fields in t-minimal theories |
| topic | Logic 03C60 |
| url | https://arxiv.org/abs/2605.06986 |