Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Formal language convexity in left-orderable groups   We propose a criterion for preserving the regularity of a formal language
representation when passing from groups to subgroups. We use this criterion to
show that the regularity of a positive cone language in a left-orderable group
passes to its finite index subgroups, and to show that there exists no left
order on a finitely generated acylindrically hyperbolic group such that the
corresponding positive cone is represented by a quasi-geodesic regular
language. We also answer one of Navas' questions by giving an example of an
infinite family of groups which admit a positive cone that is generated by
exactly $k$ generators, for every $k \geq 3$. As a special case of our
construction, we obtain a finitely generated positive cone for $F_2 \times
\mathbb{Z}$.

31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th