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arXiv · 2211.00267

Strongly minimal reducts of ACVF

Santiago Pinzon
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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 $\mathcal G=(G,\oplus,\ldots)$ 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.

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Santiago Pinzon. 2022-11-01. Strongly minimal reducts of ACVF. https://arxiv.org/abs/2211.00267

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