Fields interpretable in the free group

2020/12/28 by Rizos Sklinos, Sklinos, Rizos · 1 citation
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.2012.14468

openalex publication_date 2020/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that no infinite field is interpretable in the first-order theory of nonabelian free groups. We also obtain a characterization of Abelian groups interpretable in this theory.

Citations

• Ampleness in the free group
• Diophantine Geometry over Groups IX: Envelopes and Imaginaries

Cited by

• Algebraic groups over free and hyperbolic groups

Related

• Fields definable in the free group
• The free group does not have the finite cover property
• On groups interpretable in various valued fields
• Semisimple groups interpretable in various valued fields
• Set theory is interpretable in the automorphism group of a free group