{"paper":{"title":"Baire-class $\\xi$ colorings: the first three levels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.LO","authors_text":"Dominique Lecomte (IMJ), Miroslav Zeleny","submitted_at":"2011-04-26T08:18:14Z","abstract_excerpt":"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 $\\xi\\leq 2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.4860","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}