Strongly minimal reducts of algebraically closed valued fields
In this thesis we prove the following restricted version of Zilber's Trichotomy: Let $K=(K,+,\cdot,v,\Gamma)$ be an algebraically closed valued field and let $(G,\+)$ be a K$-definable group that is either the multiplicative group or contains a finite index subgroup that is $ K$-definably isomo...
- Autores:
-
Pinzón Palacios, Santiago Iván
- Tipo de recurso:
- Doctoral thesis
- Fecha de publicación:
- 2023
- Institución:
- Universidad de los Andes
- Repositorio:
- Séneca: repositorio Uniandes
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.uniandes.edu.co:1992/69392
- Acceso en línea:
- http://hdl.handle.net/1992/69392
- Palabra clave:
- ACVF
Zilber's Trichotomy
Valued Fields
Strongly Minimal
Matemáticas
- Rights
- openAccess
- License
- Atribución 4.0 Internacional
| Summary: | In this thesis we prove the following restricted version of Zilber's Trichotomy: Let $K=(K,+,\cdot,v,\Gamma)$ be an algebraically closed valued field and let $(G,\+)$ be a K$-definable group that is either the multiplicative group or contains a finite index subgroup that is $ K$-definably isomorphic to a $K$-definable subgroup of $(K,+)$. Then if $\mathcal G=(G,\+,\ldots)$ is a strongly minimal non locally modular structure definable in $ K$ and expanding $(G,\oplus)$, it interprets an infinite field. |
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