On algebraically closed fields with a distinguished subfield

Christian d’Elbée*, Itay Kaplan, Leor Neuhauser

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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).

Original languageAmerican English
JournalIsrael Journal of Mathematics
DOIs
StateAccepted/In press - 2024

Bibliographical note

Publisher Copyright:
© The Hebrew University of Jerusalem 2024.

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