The classification of hypersmooth Borel equivalence relations

DOI10.1090/S0894-0347-97-00221-XzbMath0865.03039OpenAlexW1860088429MaRDI QIDQ5690904

Alexander S. Kechris, Alain Louveau

Publication date: 9 January 1997

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

Full work available at URL: https://doi.org/10.1090/s0894-0347-97-00221-x

zbMATH Keywords

Borel isomorphismBorel equivalence relationsPolish spacesdichotomy theoremseffective descriptive set theoryhypersmoothBorel bi-reducibility

Mathematics Subject Classification ID

Descriptive set theory (03E15)

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Cites Work

• Unnamed Item
• Unnamed Item
• Borel transversals and ergodic measures on indecomposable continua
• Countable sections for free actions of groups
• A descriptive version of Ambrose's representation theorem for flows
• Descriptive set theory
• A Borel reductibility theory for classes of countable structures
• Borel Orderings
• Counting the number of equivalence classes of Borel and coanalytic equivalence relations
• A Glimm-Effros Dichotomy for Borel Equivalence Relations
• Countable sections for locally compact group actions
• On the Measurability of Orbits in Borel Actions
• Countable Sections for Locally Compact Group Actions. II
• The Structure of Hyperfinite Borel Equivalence Relations
• COUNTABLE BOREL EQUIVALENCE RELATIONS