Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Equations in a free group. Elementary theory   We prove the decidability of the elementary theory of a free group.

15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio