On algebraically closed fields with a distinguished subfield

Christian d'Elbée; Itay Kaplan; Leor Neuhauser

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arXiv · 2108.04160

On algebraically closed fields with a distinguished subfield

Christian d'Elbée·Itay Kaplan·Leor Neuhauser

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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, NSOP$_1$, and NIP. As an application, we conclude that a PAC field is NSOP$_1$ iff its absolute Galois group is (as a profinite group).

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BibTeX RIS

Christian d'Elbée, Itay Kaplan, Leor Neuhauser. 2021-08-09. On algebraically closed fields with a distinguished subfield. https://arxiv.org/abs/2108.04160

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