Strongly minimal reducts of ACVF

Abstract

Let $\mathbb{K}=(K,+,\cdot ,v,\Gamma )$ be a valued algebraically closed field of characteristic and $(G,\oplus )$ be a $\mathcal{K}$-interpretable group that is either locally isomorphic to $(K,+)$ or to $(K,\cdot )$. Then if $\mathcal{G}=(G,\oplus ,\dots )$ is a strongly minimal non locally modular structure intepretable in $\mathbb{K}$, it interprets a field. We also present an strategy for proving the same without the assumption of having a definable group operation.

42 pages, 5 chapters. This document is the PhD thesis of the author and it was advised by professors Alf Onshuus and Assaf Hasson