#### Volume 24, issue 3 (2020)

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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
Primary: 20F67
Secondary: 03C65