Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A partition theorem for pairs of finite sets   Every partition of [[omega_1]^{< omega}]^2 into finitely many pieces has a
cofinal homogeneous set. Furthermore, it is consistent that every directed
partially ordered set satisfies the partition property if and only if it has
finite character.

10
The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg