Baire-class $\xi$ colorings: the first three levels
Dominique Lecomte (IMJ), Miroslav Zeleny

TL;DR
This paper extends the $G_0$-dichotomy to $oraxi$-measurable countable colorings for $\xi extless= 3$, exploring their structure and providing new dichotomies for analytic relations.
Contribution
It develops a $oraxi$-measurable version of the $G_0$-dichotomy for $\xi extless= 3$, and introduces a Hurewicz-like dichotomy for unions of $oraxi$ rectangles when $\xi extless= 2.
Findings
Extended $G_0$-dichotomy to $oraxi$-measurable colorings for $\xi extless= 3$
Characterized coverings of the diagonal via countably many $oraxi$ squares
Established a Hurewicz-like dichotomy for unions of $oraxi$ rectangles when $\xi extless= 2
Abstract
The -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 -dichotomy for -measurable countable colorings when . A -measurable countable coloring gives a covering of the diagonal consisting of countably many squares. This leads to the study of countable unions of rectangles. We also give a Hurewicz-like dichotomy for such countable unions when .
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Taxonomy
TopicsAdvanced Topology and Set Theory · Advanced Operator Algebra Research · Advanced Banach Space Theory
