Some lower bounds on Shelah rank in the free group

@article{Gonzalez2020SomeLB,
title={Some lower bounds on Shelah rank in the free group},
author={Javier Gonz'alez and Chlo{\'e} Perin and Rizos Sklinos},
journal={Ann. Pure Appl. Log.},
year={2020},
volume={171},
pages={102794}
}

In this short note it is proved that a definable set X over $\mathbb F_n$ is superstable only if X(F_n) = X (Mathbb F_{\omega}) if and only if the set is definable.Expand

We consider embeddings in a torsion-free hyperbolic group which are elementary in the sense of first-order logic. We give a description of these embeddings in terms of Sela's hyperbolic towers. We… Expand

Preface Conventions 1. Groups and graphs 2. Cutting graphs and building trees 3. The almost stability theorem 4. Applications of the almost stability theorem 5. Poincare duality 6. Two-dimensional… Expand

This paper is the eighth in a sequence on the structure of sets of solutions to systems of equations in free and hyperbolic groups, projections of such sets (Diophantine sets), and the structure of… Expand

Abstract.This paper is the sixth in a sequence on the structure of sets of solutions to systems of equations in a free group, projections of such sets, and the structure of elementary sets defined… Expand

A quasi-tree is a geodesic metric space quasi-isometric to a tree. We give a general construction of many actions of groups on quasi-trees. The groups we can handle include non-elementary… Expand

This paper is the first in a sequence on the structure of sets of solutions to systems of equations in a free group, projections of such sets, and the structure of elementary sets defined over a free… Expand