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 $\mathcal{G}=(G,\oplus ,\dots )$ 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.

arXiv admin note: text overlap with arXiv:2211.00267