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.

scholarly journals On Borel equivalence relations in generalized Baire space

2012 ◽  
Vol 51 (3-4) ◽  
pp. 299-304 ◽  
Author(s):  
Sy-David Friedman ◽  
Tapani Hyttinen
Keyword(s):  
Baire Space ◽  
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.

COUNTABLE BOREL EQUIVALENCE RELATIONS

2002 ◽  
Vol 02 (01) ◽  
pp. 1-80 ◽  
Author(s):  
S. JACKSON ◽  
A. S. KECHRIS ◽  
A. LOUVEAU
Keyword(s):  
Set Theory ◽  
Equivalence Relations ◽  
Descriptive Set Theory ◽  
Polish Spaces ◽  
Borel Equivalence Relations ◽  
Universal Equivalence ◽  
Descriptive Set

This paper develops the foundations of the descriptive set theory of countable Borel equivalence relations on Polish spaces with particular emphasis on the study of hyperfinite, amenable, treeable and universal equivalence relations.

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