Submission date: 30 August 2023

Abstract:

Let 𝕂=(K,+,×,v,Γ) be an algebraically closed valued field and let (G,+) be a 𝕂-definable group that is either the multiplicative group or contains a finite index subgroup that is \mathbb K-definably isomorphic to a 𝕂-definable subgroup of (K,+). Then if 𝔾=(G,+,...) is a strongly minimal non locally modular structure definable in 𝕂 and expanding (G,⊕), 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.

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Full text arXiv : 2308.16133 pdf, ps.