{"paper":{"title":"Borel partitions of infinite subtrees of a perfect tree","license":"","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Alain Louveau, Boban Veli\\v{c}kovi\\'c, Saharon Shelah","submitted_at":"1993-01-15T00:00:00Z","abstract_excerpt":"A theorem of Galvin asserts that if the unordered pairs of reals are partitioned into finitely many Borel classes then there is a perfect set P such that all pairs from P lie in the same class. The generalization to n-tuples for n >= 3 is false. Let us identify the reals with 2^omega ordered by the lexicographical ordering and define for distinct x,y in 2^omega, D(x,y) to be the least n such that x(n) not= y(n). Let the type of an increasing n-tuple {x_0, ... x_{n-1}}_< be the ordering <^* on {0, ...,n-2} defined by i<^*j iff D(x_i,x_{i+1})< D(x_j,x_{j+1}). Galvin proved that for any Borel col"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9301209","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"}