Strongly minimal reducts of ACVF

Abstract

In this document we prove: Let $\mathbb K=(K,+,\cdot,v,\Gamma)$ be an algebraically closed valued field and let $(G,\oplus)$ be a $\mathbb K$-definable group that is either the multiplicative group or contains a finite index subgroup that is $\mathbb K$-definably isomorphic to a $\mathbb K$-definable subgroup of $(K,+)$. Then if $\mathcal G=(G,\oplus,\ldots)$ is a strongly minimal non locally modular structure definable in $\mathbb K$ and expanding $(G,\oplus)$, it interprets an infinite field. This document is the PhD thesis of the author and it was advised by professors Assaf Hasson and Alf Onshuus.