Strongly minimal reducts of algebraically closed valued fields

• Autores: Santiago Iván Pinzón Palacios
• Directores de la Tesis: Alf Onshuus (dir. tes.), Assaf Hasson (dir. tes.)
• Lectura: En la Universidad de los Andes (Colombia) ( Colombia ) en 2023
• Idioma: inglés
• Tribunal Calificador de la Tesis: Pablo Cubides (presid.), Kobi Peterzil (presid.), Piotr Kowalski (presid.)
• Enlaces
  • Tesis en acceso abierto en: hdl.handle.net
• Resumen

  • 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.