Submission date: 9 August 2021

Abstract:

This paper is concerned with the model-theoretic study of pairs (K,F) where K is 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, NSOP_1, and NIP. As an application, we conclude that a field is NSOP_1 iff its absolute Galois group is (as a profinite group).

Mathematics Subject Classification: 03C45, 03C10, 03C60

Keywords and phrases:

Full text arXiv 2108.04160: pdf, ps.