Mathematics > Logic
[Submitted on 9 Aug 2021 (v1), last revised 24 Aug 2022 (this version, v5)]
Title:On algebraically closed fields with a distinguished subfield
View PDFAbstract: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).
Submission history
From: Leor Neuhauser [view email][v1] Mon, 9 Aug 2021 16:34:03 UTC (31 KB)
[v2] Tue, 10 Aug 2021 09:21:49 UTC (31 KB)
[v3] Wed, 22 Sep 2021 14:17:32 UTC (32 KB)
[v4] Tue, 5 Oct 2021 18:19:45 UTC (32 KB)
[v5] Wed, 24 Aug 2022 17:59:25 UTC (33 KB)
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