Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebraically Closed Fields with a Generic Multiplicative Character   We study the model theory of the $2$-sorted structure $(\mathbb{F},
\mathbb{C};\chi)$, where $\mathbb{F}$ is an algebraic closure of a finite field
of characteristic $p$, $\mathbb{C}$ is the field of complex numbers and $\chi:
\mathbb{F} \to \mathbb{C}$ is an injective, multiplication preserving map. We
obtain an axiomatization $\mathrm{ACFC}_p$ of
$\mathrm{Th}(\mathbb{F},\mathbb{C};\chi)$ in a suitable language $L$, classify
the models of $\mathrm{ACFC}_p$ up to isomorphism, prove a modified model
companion result, give various descriptions of definable sets inside a model of
$\mathrm{ACFC}_p$, and deduce that $\mathrm{ACFC}_p$ is $\omega$-stable and has
definability of Morley rank in families.

37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn