Decidability of the Elementary Theory of a Torsion-Free Hyperbolic Group

Abstract

Let G be a torsion free hyperbolic group. We prove that the elementary theory of G is decidable and admits an effective quantifier elimination to boolean combination of AE-formulas. The existence of such quantifier elimination was previously proved by Sela.

Misprints and errors corrected, referee suggestions addressed. arXiv admin note: substantial text overlap with arXiv:1207.1900

References in corpus (2)

• Strong accessibility for finitely presented groups
• Quantifier elimination algorithm to boolean combination of $\exists \forall$-formulas in the theory of a free group

Cited by in corpus (6)

• The triviality problem for profinite completions
• On the model theory of higher rank arithmetic groups
• On groups elementarily equivalent to a group of triangular matrices $T_n(R)$
• On Tarski's Decidability Problem
• A report on Tarski's decidability problem
• On fully residually-$\mathcal{R}$ groups