Decidability of the Elementary Theory of a Torsion-Free Hyperbolic Group
Olga Kharlampovich, Alexei Myasnikov
TL;DR
This paper proves that the elementary theory of torsion-free hyperbolic groups is decidable and can be effectively simplified to boolean combinations of AE-formulas, building on Sela's prior work.
Contribution
It establishes the decidability and effective quantifier elimination for the elementary theory of torsion-free hyperbolic groups, advancing understanding of their logical properties.
Findings
Elementary theory of G is decidable
Quantifier elimination to boolean combinations of AE-formulas
Builds on Sela's previous results
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.
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Taxonomy
TopicsGeometric and Algebraic Topology · Mathematical Dynamics and Fractals · Homotopy and Cohomology in Algebraic Topology