A dichotomy characterizing analytic digraphs of uncountable Borel chromatic number in any dimension

DOI10.1090/S0002-9947-09-04792-8zbMath1169.03037arXiv0707.1313MaRDI QIDQ5322890

Dominique Lecomte

Publication date: 23 July 2009

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0707.1313

zbMATH Keywords

dimensionfinite dimensioninfinite dimensionBorel chromatic numberanalytic graphsKechris-Solecki-Todorčević dichotomy

Mathematics Subject Classification ID

Descriptive set theory (03E15) Coloring of graphs and hypergraphs (05C15)

Related Items (9)

Borel chromatic number of closed graphs ⋮ Injective tests of low complexity in the plane ⋮ Dichotomy theorems for countably infinite dimensional analytic hypergraphs ⋮ Baire-class $\xi $ colorings: The first three levels ⋮ The graph-theoretic approach to descriptive set theory ⋮ Polishness of some topologies related to word or tree automata ⋮ On the complexity of Borel equivalence relations with some countability property ⋮ A SEPARATION RESULT FOR COUNTABLE UNIONS OF BOREL RECTANGLES ⋮ Potential Wadge classes

Cites Work

• Descriptive set theory
• Borel chromatic numbers
• A Glimm-Effros Dichotomy for Borel Equivalence Relations
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