On the complexity of the isomorphism relation for finitely generated groups

被引：37

作者：

Thomas, S ^{[1
]}

Velickovic, B

机构：

[1] Rutgers State Univ, Dept Math, New Brunswick, NJ 08903 USA

[2] Univ Paris 07, Equipe Log, URA 753, F-75251 Paris, France

来源：

JOURNAL OF ALGEBRA | 1999年 / 217卷 / 01期

基金：

美国国家科学基金会;

关键词：

D O I：

10.1006/jabr.1998.7825

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Confirming a conjecture of G. Hjorth and A. Kechris (1996, Ann. Pure Appl. Logic 82, 221-272) we prove that the isomorphism relation for finitely generated groups is a universal essentially countable Borel equivalence relation. We also prove the corresponding result for the conjugacy relation for subgroups of the free group F-2 On two generators. (C) 1999 Academic Press.

引用

页码：352 / 373

页数：22

共 16 条

[1]

BECKER H, 1997, LONDON MATH SOC LECT

[2] THE STRUCTURE OF HYPERFINITE BOREL EQUIVALENCE-RELATIONS [J].

DOUGHERTY, R ;

JACKSON, S ;

KECHRIS, AS .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1994, 341 (01) :193-225

[3] ERGODIC EQUIVALENCE RELATIONS, COHOMOLOGY, AND VONNEUMANN ALGEBRAS .1. [J].

FELDMAN, J ;

MOORE, CC .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1977, 234 (02) :289-324

[4] A BOREL REDUCIBILITY THEORY FOR CLASSES OF COUNTABLE STRUCTURES [J].

FRIEDMAN, H ;

STANLEY, L .

JOURNAL OF SYMBOLIC LOGIC, 1989, 54 (03) :894-914

[5]

FUCHS L, 1967, ABELIAN GROUPS

[6] Borel equivalence relations and classifications of countable models [J].

Hjorth, G ;

Kechris, AS .

ANNALS OF PURE AND APPLIED LOGIC, 1996, 82 (03) :221-272

[7]

HJORTH G, 1998, NONCLASSIFIABILITY C

[8]

JACKSON S, UNPUB COUNTABLE BORE

[9] FREE PRODUCT OF 2 GROUPS WITH A MALNORMAL AMALGAMATED SUBGROUP [J].

KARRASS, A ;

SOLITAR, D .

CANADIAN JOURNAL OF MATHEMATICS, 1971, 23 (06) :933-&

[10]

Kechris, 2012, CLASSICAL DESCRIPTIV, V156

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