Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Baire class one colorings and a dichotomy for countable unions of
  $F_\sigma$ rectangles   We study the Baire class one countable colorings, i.e., the countable
partitions into $F_\sigma$ sets. Such a partition gives a covering of the
diagonal into countably many $F_\sigma$ squares. This leads to the study of
countable unions of $F_\sigma$ rectangles. We give a Hurewicz-like dichotomy
for such countable unions.

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The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: chem-ph