Baire class one colorings and a dichotomy for countable unions of $F_σ$ rectangles

Details Baire class one colorings and a dichotomy for countable unions of $F_σ$ rectangles Baire class one colorings and a dichotomy for countable unions of $F_σ$ rectangles

2010-04-13

arxiv.org/abs/1004.2172v1

Mathematics

Logic

Scientific paper

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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