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Strongly minimal reducts of ACVF

Logic 2023-09-20 v2

Abstract

In this document we prove: Let K=(K,+,,v,Γ)\mathbb K=(K,+,\cdot,v,\Gamma) be an algebraically closed valued field and let (G,)(G,\oplus) be a K\mathbb K-definable group that is either the multiplicative group or contains a finite index subgroup that is K\mathbb K-definably isomorphic to a K\mathbb K-definable subgroup of (K,+)(K,+). Then if G=(G,,)\mathcal G=(G,\oplus,\ldots) is a strongly minimal non locally modular structure definable in K\mathbb K and expanding (G,)(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.

Keywords

Cite

@article{arxiv.2308.16133,
  title  = {Strongly minimal reducts of ACVF},
  author = {Santiago Pinzon},
  journal= {arXiv preprint arXiv:2308.16133},
  year   = {2023}
}

Comments

arXiv admin note: text overlap with arXiv:2211.00267