Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characterizing the existence of a Borel complete expansion   We develop general machinery to cast the class of potential canonical Scott
sentences of an infinitary sentence $\Phi$ as a class of structures in a
related language. From this, we show that $\Phi$ has a Borel complete expansion
if and only if $S_\infty$ divides $Aut(M)$ for some countable model $M\models
\Phi$. Using this, we prove that for theories $T_h$ asserting that $\{E_n\}$ is
a countable family of cross cutting equivalence relations with $h(n)$ classes,
if $h(n)$ is uniformly bounded then $T_h$ is not Borel complete, providing a
converse to Theorem~2.1 of \cite{LU}.

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The categories of this paper are: supr-con
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The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: stat
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The categories of this paper are: nlin
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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: econ