Baire-class $ξ$ colorings: the first three levels

Details Baire-class $ξ$ colorings: the first three levels Baire-class $ξ$ colorings: the first three levels

2011-04-26

arxiv.org/abs/1104.4860v1

Mathematics

Logic

Scientific paper

The $\mathbb{G}_0$-dichotomy due to Kechris, Solecki and Todor\vcevi\'c characterizes the analytic relations having a Borel-measurable countable coloring. We give a version of the $\mathbb{G}_0$-dichotomy for $\boraxi$-measurable countable colorings when $\xi\leq 3$. A $\boraxi$-measurable countable coloring gives a covering of the diagonal consisting of countably many $\boraxi$ squares. This leads to the study of countable unions of $\boraxi$ rectangles. We also give a Hurewicz-like dichotomy for such countable unions when $\xi\leq 2$.

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