Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rooted trees, strong cofinality and ample generics   We characterize those countable rooted trees whose full automorphism group
has uncountable strong cofinality or contains an open subgroup with ample
generics.

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The categories of this paper are: hep-th
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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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: cs
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio