Analytic equivalence relations and bi-embeddability

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

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

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 76,140

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

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
2013-09-30

Downloads
8 (#987,925)

6 months
1 (#447,993)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

References found in this work

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

Add more references