Free and Hyperbolic Groups are not Equational

2012/04/23 by Zlil Sela, Sela, Z.
Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Logic (math.LO) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1204.5075

openalex publication_date 2012/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an example of a definable set in every free or torsion-free (non-elementary) hyperbolic group that is not in the Boolean algebra of equational sets. Hence, the theories of free and torsion-free (non-elementary) hyperbolic groups are not equational in the sense of G. Srour.

Citations

• Diophantine Geometry over Groups IX: Envelopes and Imaginaries

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