Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $2^{\aleph_0}$ pairwise non-isomorphic maximal-closed subgroups of
  Sym$(\mathbb{N})$ via the classification of the reducts of the Henson
  digraphs   Given two structures $\mathcal{M}$ and $\mathcal{N}$ on the same domain, we
say that $\mathcal{N}$ is a reduct of $\mathcal{M}$ if all
$\emptyset$-definable relations of $\mathcal{N}$ are $\emptyset$-definable in
$\mathcal{M}$. In this article the reducts of the Henson digraphs are
classified. Henson digraphs are homogeneous countable digraphs that omit some
set of finite tournaments. As the Henson digraphs are $\aleph_0$-categorical,
determining their reducts is equivalent to determining all closed supergroups
$G<$ Sym$(\mathbb{N})$ of their automorphism groups.
  A consequence of the classification is that there are $2^{\aleph_0}$ pairwise
non-isomorphic Henson digraphs which have no proper non-trivial reducts. Taking
their automorphisms groups gives a positive answer to a question of Macpherson
that asked if there are $2^{\aleph_0}$ pairwise non-conjugate maximal-closed
subgroups of Sym$(\mathbb{N})$. By the reconstruction results of Rubin, these
groups are also non-isomorphic as abstract groups.

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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: cs
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: hep-ph
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: nlin