Hyperbolicity and Cubulability Are Preserved Under Elementary Equivalence
Group Theory
2020-10-07 v1 Logic
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 property, then G enjoys this property as well.
Cite
@article{arxiv.1801.09411,
title = {Hyperbolicity and Cubulability Are Preserved Under Elementary Equivalence},
author = {Simon André},
journal= {arXiv preprint arXiv:1801.09411},
year = {2020}
}