1998/12/14 by Olga Kharlampovich, Alexei Myasnikov · 2 citations
Mathematics · #Geometric and Algebraic Topology #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology #Elementary theory #Mathematics #Decidability #Group (periodic table) #Elementary proof #Model theory #Infinite group #Free group #Group theory #Pure mathematics #Algebra over a field #Discrete mathematics #Quantum mechanics #Physics #Computer science
paper · pdf · doi:10.1090/s1079-6762-98-00047-x
openalex publication_date 1998/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
We prove that the elementary theories of all nonabelian free groups coincide and that the elementary theory of a free group is decidable. These results answer two old questions that were raised by A. Tarski around 1945.