Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonequational Stable Groups   We introduce a combinatorial criterion for verifying whether a formula is not
the conjunction of an equation and a co-equation. Using this, we give a
transparent proof for the nonequationality of the free group, which was
originally proved by Sela. Furthermore, we extend this result to arbitrary free
products of groups (except $\mathbb{Z}_2*\mathbb{Z}_2$), providing an abundance
of new stable nonequational theories.

34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
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The categories of this paper are: dg-ga
1
The categories of this paper are: cs
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The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
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The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph