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Preprint Number 2291

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2291. Santiago Pinzon
Strongly minimal reducts of ACVF

Submission date: 1 November 2022.


This document is the PhD thesis of the author and it was advised by professors Alf Onshuus and Assaf Hasson.

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

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