Recent developments in the theory of Borel reducibility

• Autorzy: Greg Hjorth , Alexander S. Kechris
• Języki publikacji: EN

Abstrakty

EN

Let E₀ be the Vitali equivalence relation and E₃ the product of countably many copies of E₀. Two new dichotomy theorems for Borel equivalence relations are proved. First, for any Borel equivalence relation E that is (Borel) reducible to E₃, either E is reducible to E₀ or else E₃ is reducible to E. Second, if E is a Borel equivalence relation induced by a Borel action of a closed subgroup of the infinite symmetric group that admits an invariant metric, then either E is reducible to a countable Borel equivalence relation or else E₃ is reducible to E.
We also survey a number of results and conjectures concerning the global structure of reducibility on Borel equivalence relations.

Kategorie tematyczne

• 03E15: Descriptive set theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2001
• Tom: 170
• Numer: 1-2
• Strony: 21-52

Daty

wydano

2001

Twórcy

autor

Greg Hjorth

• Department of Mathematics, UCLA, Los Angeles, CA 90095-1555, U.S.A.

autor

Alexander S. Kechris

• Department of Mathematics, Caltech, Pasadena, CA 91125, U.S.A.

Identyfikatory

DOI

10.4064/fm170-1-2