Greg Hjorth and Alexander S. Kechris. Analytic equivalence relations and Ulm-type classifications. The journal of symbolic logic, vol. 60 (1995), pp. 1273–1300. - Greg Hjorth, Alexander S. Kechris, and Alain Louveau. Borel equivalence relations induced by actions of the symmetric group. Annals of pure and applied logic, vol. 92 (1998), pp. 63–112.

2001 ◽  
Vol 7 (4) ◽  
pp. 541-544
Author(s):  
Sławomir Solecki
Keyword(s):  
Symmetric Group ◽  
Equivalence Relations ◽  
Symbolic Logic ◽  
Applied Logic ◽  
Borel Equivalence Relations

scholarly journals Borel equivalence relations induced by actions of the symmetric group

1998 ◽  
Vol 92 (1) ◽  
pp. 63-112 ◽  
Author(s):  
Greg Hjorth ◽  
Alexander S. Kechris ◽  
Alain Louveau
Keyword(s):  
Symmetric Group ◽  
Equivalence Relations ◽  
Borel Equivalence Relations

James Cummings and Ernest Schimmerling, editors. Lecture Note Series of the London Mathematical Society, vol. 406. Cambridge University Press, New York, xi + 419 pp. - Paul B. Larson, Peter Lumsdaine, and Yimu Yin. An introduction to Pmax forcing. pp. 5–23. - Simon Thomas and Scott Schneider. Countable Borel equivalence relations. pp. 25–62. - Ilijas Farah and Eric Wofsey. Set theory and operator algebras. pp. 63–119. - Justin Moore and David Milovich. A tutorial on set mapping reflection. pp. 121–144. - Vladimir G. Pestov and Aleksandra Kwiatkowska. An introduction to hyperlinear and sofic groups. pp. 145–185. - Itay Neeman and Spencer Unger. Aronszajn trees and the SCH. pp. 187–206. - Todd Eisworth, Justin Tatch Moore, and David Milovich. Iterated forcing and the Continuum Hypothesis. pp. 207–244. - Moti Gitik and Spencer Unger. Short extender forcing. pp. 245–263. - Alexander S. Kechris and Robin D. Tucker-Drob. The complexity of classification problems in ergodic theory. pp. 265–299. - Menachem Magidor and Chris Lambie-Hanson. On the strengths and weaknesses of weak squares. pp. 301–330. - Boban Veličković and Giorgio Venturi. Proper forcing remastered. pp. 331–362. - Asger ToÖrnquist and Martino Lupini. Set theory and von Neumann algebras. pp. 363–396. - W. Hugh Woodin, Jacob Davis, and Daniel RodrÍguez. The HOD dichotomy. pp. 397–419.

2014 ◽  
Vol 20 (1) ◽  
pp. 94-97
Author(s):  
Natasha Dobrinen
Keyword(s):  
New York ◽  
Set Theory ◽  
Von Neumann Algebras ◽  
Operator Algebras ◽  
Continuum Hypothesis ◽  
London Mathematical Society ◽  
Equivalence Relations ◽  
Classification Problems ◽  
Von Neumann ◽  
Borel Equivalence Relations

EMBEDDINGS OF P(ω)/Fin INTO BOREL EQUIVALENCE RELATIONS BETWEEN ℓp AND ℓq

2015 ◽  
Vol 80 (3) ◽  
pp. 917-939 ◽  
Author(s):  
ZHI YIN
Keyword(s):  
Partially Ordered Set ◽  
Ordered Set ◽  
Equivalence Relations ◽  
Borel Equivalence Relations ◽  
Partially Ordered

AbstractWe prove that, for 1 ≤ p < q < ∞, the partially ordered set P(ω)/Fin can be embedded into Borel equivalence relations between ℝω/ℓp and ℝω/ℓq. Since there is an antichain of size continuum in P(ω)/Fin, there are continuum many pairwise incomparable Borel equivalence relations between ℝω/ℓp and ℝω/ℓq.

FAILURES OF THE SILVER DICHOTOMY IN THE GENERALIZED BAIRE SPACE

2015 ◽  
Vol 80 (2) ◽  
pp. 661-670 ◽  
Author(s):  
SY-DAVID FRIEDMAN ◽  
VADIM KULIKOV
Keyword(s):  
Baire Space ◽  
Equivalence Relations ◽  
Borel Equivalence Relations

AbstractWe prove results that falsify Silver’s dichotomy for Borel equivalence relations on the generalized Baire space under the assumptionV=L.

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