Recent developments in the theory of Borel reducibility

Greg Hjorth, and Alexander S. Kechris. "Recent developments in the theory of Borel reducibility." Fundamenta Mathematicae 170.1-2 (2001): 21-52. <http://eudml.org/doc/281714>.

@article{GregHjorth2001,
abstract = { 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. },
author = {Greg Hjorth, Alexander S. Kechris},
journal = {Fundamenta Mathematicae},
keywords = {Borel equivalence relation; Borel reducibility; dichotomy theorems},
language = {eng},
number = {1-2},
pages = {21-52},
title = {Recent developments in the theory of Borel reducibility},
url = {http://eudml.org/doc/281714},
volume = {170},
year = {2001},
}

TY - JOUR
AU - Greg Hjorth
AU - Alexander S. Kechris
TI - Recent developments in the theory of Borel reducibility
JO - Fundamenta Mathematicae
PY - 2001
VL - 170
IS - 1-2
SP - 21
EP - 52
AB - 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.
LA - eng
KW - Borel equivalence relation; Borel reducibility; dichotomy theorems
UR - http://eudml.org/doc/281714
ER -