Journal of Symbolic Logic 76 (1):243 - 266 (2011)

Authors
Abstract
Louveau and Rosendal [5] have shown that the relation of bi-embeddability for countable graphs as well as for many other natural classes of countable structures is complete under Borel reducibility for analytic equivalence relations. This is in strong contrast to the case of the isomorphism relation, which as an equivalence relation on graphs (or on any class of countable structures consisting of the models of a sentence of L ω ₁ ω ) is far from complete (see [5, 2]). In this article we strengthen the results of [5] by showing that not only does bi-embeddability give rise to analytic equivalence relations which are complete under Borel reducibility, but in fact any analytic equivalence relation is Borel equivalent to such a relation. This result and the techniques introduced answer questions raised in [5] about the comparison between isomorphism and bi-embeddability. Finally, as in [5] our results apply not only to classes of countable structures defined by sentences of ω ₁ ω , but also to discrete metric or ultrametric Polish spaces, compact metrizable topological spaces and separable Banach spaces, with various notions of embeddability appropriate for these classes, as well as to actions of Polish monoids
Keywords Analytic equivalence relation   analytic quasi-order   bi-embeddability   Borel reducibility
Categories (categorize this paper)
DOI 10.2178/jsl/1294170999
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 58,518
Through your library

References found in this work BETA

[Omnibus Review].Yiannis N. Moschovakis - 1968 - Journal of Symbolic Logic 33 (3):471-472.

Add more references

Citations of this work BETA

Polish Metric Spaces with Fixed Distance Set.Riccardo Camerlo, Alberto Marcone & Luca Motto Ros - 2020 - Annals of Pure and Applied Logic 171 (10):102832.

Add more citations

Similar books and articles

Infinite Time Decidable Equivalence Relation Theory.Samuel Coskey & Joel David Hamkins - 2011 - Notre Dame Journal of Formal Logic 52 (2):203-228.
Actions of Non-Compact and Non-Locally Compact Polish Groups.Sławomir Solecki - 2000 - Journal of Symbolic Logic 65 (4):1881-1894.
Classifying Positive Equivalence Relations.Claudio Bernardi & Andrea Sorbi - 1983 - Journal of Symbolic Logic 48 (3):529-538.
Borel Structures and Borel Theories.Greg Hjorth & André Nies - 2011 - Journal of Symbolic Logic 76 (2):461 - 476.
Borel Equivalence Relations Which Are Highly Unfree.Greg Hjorth - 2008 - Journal of Symbolic Logic 73 (4):1271-1277.
Diagonal Actions and Borel Equivalence Relations.Longyun Ding & Su Gao - 2006 - Journal of Symbolic Logic 71 (4):1081 - 1096.
On Σ1 1 Equivalence Relations with Borel Classes of Bounded Rank.Ramez L. Sami - 1984 - Journal of Symbolic Logic 49 (4):1273 - 1283.
? 0 N -Equivalence Relations.Andrea Sorbi - 1982 - Studia Logica 41 (4):351-358.

Analytics

Added to PP index
2013-09-30

Total views
6 ( #1,077,288 of 2,421,640 )

Recent downloads (6 months)
1 ( #545,272 of 2,421,640 )

How can I increase my downloads?

Downloads

My notes