vix.ing · top · new · best · stats · spec

Strongly minimal reducts of ACVF

2022/11/01 by Santiago Pinzón, Pinzon, Santiago
Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2211.00267

openalex publication_date 2022/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \mathbb K=(K,+,⋅,v,Γ) be a valued algebraically closed field of characteristic and (G,⊕) be a \mathcal K-interpretable group that is either locally isomorphic to (K,+) or to (K,⋅). Then if \mathcal G=(G,⊕,…) 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.

Related