Towers and the First-Order Theories of Hyperbolic Groups

Devoted to the first-order theories of torsion-free hyperbolic groups, one of the purposes of this paper is to review some results and to provide precise and correct statements and definitions, as well as some proofs and new results. A key concept is that of a tower (Sela) or NTQ system (Kharlampovich-Myasnikov). We discuss them thoroughly.

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