Stability and Bounded Balls of Free Products
Logic
2009-01-22 v1 Group Theory
Abstract
In a series of papers starting in [Sel01] and culminating in [Sel07], Z. Sela proved that free groups, and more generally torsion-free hyperbolic groups, have a stable first-order theory. The question of the stability of the free product of two arbitrary stable groups has then been raised by E. Jaligot with, seemingly, the reasonable conjecture of a positive answer [Jal08]. The complete proof however will be a grand project of generalization of above papers of Sela.In the meantime, we provide here a very preliminary -or somehow experi- mental- result in the direction of the stability of free products of stable groups, restricting ourselves to quantifer-free definable sets and to bounded balls of free products.
Cite
@article{arxiv.0901.3212,
title = {Stability and Bounded Balls of Free Products},
author = {Azadeh Neman},
journal= {arXiv preprint arXiv:0901.3212},
year = {2009}
}