Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $X$-torsion and universal groups   For a set $X\subseteq \mathbb{N}$, we define the $X$-torsion of a group $G$
to be all elements $g\in G$ with $g^{n}=e$ for some $n\in X$. With $X$
recursively enumerable, we give two independent proofs (group-theoretic, and
model-theoretic) that there exists a universal finitely presented
$X$-torsion-free group; one which contains all finitely presented
$X$-torsion-free groups. We also show that, if $X$ is recursively enumerable,
then the set of finite presentations of $X$-torsion-free groups is
$\Pi_{2}^{0}$-complete in Kleene's arithmetic hierarchy.

30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex