Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On algebraically closed fields with a distinguished subfield   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).

17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph