English

Strongly minimal reducts of ACVF

Logic 2022-11-02 v1

Abstract

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

Keywords

Cite

@article{arxiv.2211.00267,
  title  = {Strongly minimal reducts of ACVF},
  author = {Santiago Pinzon},
  journal= {arXiv preprint arXiv:2211.00267},
  year   = {2022}
}

Comments

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