Volume 24, issue 3 (2020)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 26
Issue 7, 2855–3306
Issue 6, 2405–2853
Issue 5, 1907–2404
Issue 4, 1435–1905
Issue 3, 937–1434
Issue 2, 477–936
Issue 1, 1–476

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Hyperbolicity and cubulability are preserved under elementary equivalence

Simon André

Geometry & Topology 24 (2020) 1075–1147
Abstract

The following properties are preserved under elementary equivalence, among finitely generated groups: being hyperbolic (possibly with torsion), being hyperbolic and cubulable, and being a subgroup of a hyperbolic group. In other words, if a finitely generated group G has the same first-order theory as a group possessing one of the previous properties, then G enjoys that property as well.

Keywords
hyperbolic groups, cubulable groups, model theory, elementary equivalence, first-order logic
Mathematical Subject Classification 2010
Primary: 20F67
Secondary: 03C65
References
Publication
Received: 14 February 2018
Revised: 23 April 2019
Accepted: 13 July 2019
Published: 30 September 2020
Proposed: Martin Bridson
Seconded: Anna Wienhard, Walter Neumann
Authors
Simon André
Université de Rennes 1
CNRS
IRMAR-UMR 6625
Rennes
France
Department of Mathematics
Vanderbilt University
Nashville, TN
United States