Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Formal solutions and the first-order theory of acylindrically hyperbolic
  groups   We generalise Merzlyakov's theorem about the first-order theory of
non-abelian free groups to all acylindrically hyperbolic groups. As a
corollary, we deduce that if $G$ is an acylindrically hyperbolic group and
$E(G)$ denotes the unique maximal finite normal subgroup of $G$, then $G$ and
the HNN extension $G\dot{\ast}_{E(G)}$, which is simply the free product
$G\ast\mathbb{Z}$ when $E(G)$ is trivial, have the same
$\forall\exists$-theory. As a consequence, we prove the following conjecture,
formulated by Casals-Ruiz, Garreta and de la Nuez Gonz\'alez: acylindrically
hyperbolic groups have trivial positive theory. In particular, one recovers a
result proved by Bestvina, Bromberg and Fujiwara, stating that, with only the
obvious exceptions, verbal subgroups of acylindrically hyperbolic groups have
infinite width.

33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph