{"paper":{"title":"Borel structurability on the 2-shift of a countable group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.DS","authors_text":"Brandon Seward, Robin D. Tucker-Drob","submitted_at":"2014-02-17T23:51:16Z","abstract_excerpt":"We show that for any infinite countable group $G$ and for any free Borel action $G \\curvearrowright X$ there exists an equivariant class-bijective Borel map from $X$ to the free part $\\mathrm{Free}(2^G)$ of the $2$-shift $G \\curvearrowright 2^G$. This implies that any Borel structurability which holds for the equivalence relation generated by $G \\curvearrowright \\mathrm{Free}(2^G)$ must hold a fortiori for all equivalence relations coming from free Borel actions of $G$. A related consequence is that the Borel chromatic number of $\\mathrm{Free}(2^G)$ is the maximum among Borel chromatic numbers"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.4184","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"}