Towers and the First-Order Theories of Hyperbolic Groups

Vincent Guirardel, University of Rennes, France, Gilbert Levitt, Universite de Caen, France, and Rizos Sklinos, Chinese Academy of Sciences, Beijing, People's Republic of China.

1. Introduction 2. Overview of the paper 3. Preliminaries 4. Towers 5. Some properties of towers 6. Towers as an ordering: core and prototypes 7. Elementary equivalence of torsion-free hyperbolic groups 8. Elementary embeddings 9. Partial elementary maps extend to the relative core 10. Examples and counterexamples 11. Minimal and maximal models A. Appendix: Towers are limit groups