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Diophantine geometry over groups and the elementary theory of free and hyperbolic groups. (English) Zbl 1060.20022
Li, Ta Tsien (ed.) et al., Proceedings of the international congress of mathematicians, ICM 2002, Beijing, China, August 20–28, 2002. Vol. II: Invited lectures. Beijing: Higher Education Press; Singapore: World Scientific/distributor (ISBN 7-04-008690-5/3-vol. set). 87-92 (2002).

20E05 Free nonabelian groups
03C07 Basic properties of first-order languages and structures
03C60 Model-theoretic algebra
20A15 Applications of logic to group theory
14A22 Noncommutative algebraic geometry
20F05 Generators, relations, and presentations of groups
20F65 Geometric group theory
20F67 Hyperbolic groups and nonpositively curved groups
57M07 Topological methods in group theory