2021/08/09 by Christian d’Elbée, d'Elbée, Christian, Itay Kaplan +3
Mathematics · #03C10 #03C45 #03C60 #Advanced Topology and Set Theory #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO)
paper · pdf · doi:10.48550/arxiv.2108.04160
openalex publication_date 2021/08/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is concerned with the model-theoretic study of pairs (K,F) where K is an algebraically closed field and F is a distinguished subfield of K allowing extra structure. We study the basic model-theoretic properties of those pairs, such as quantifier elimination, model-completeness and saturated models. We also prove some preservation results of classification-theoretic notions such as stability, simplicity, NSOP1, and NIP. As an application, we conclude that a PAC field is NSOP1 iff its absolute Galois group is (as a profinite group).