Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: No positive cone in a free product is regular   We show that there exists no left order on the free product of two
nontrivial, finitely generated, left-orderable groups such that the
corresponding positive cone is represented by a regular language. Since there
are orders on free groups of rank at least two with positive cone languages
that are context-free (in fact, 1-counter languages), our result provides a
bound on the language complexity of positive cones in free products that is the
best possible within the Chomsky hierarchy. It also provides a strengthening of
a result by Cristobal Rivas stating that the positive cone in a free product of
nontrivial, finitely generated, left-orderable groups cannot be finitely
generated as a semigroup.

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The categories of this paper are: stat
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The categories of this paper are: cs
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int