35 citations · 54 across the 10 of their papers we have counts for
11 papers
Algebraic groups over free and hyperbolic groups
Vincent Guirardel, Chloé Perin
We define an algebraic group over a group to be a variety - that is, a subset of defined by equations over - endowed with a group law whose coordinates can be express…
Homogeneity of torsion-free hyperbolic groups
Ayala Dente-Byron, Chloé Perin
We give a complete characterization of torsion-free hyperbolic groups which are homogeneous in the sense of first-order logic, in terms of the JSJ decompositions of their free fact…
Elementary subgroups of the free group are free factors - a new proof
Chloé Perin
In this note we give a new proof of the fact that an elementary subgroup (in the sense of first-order theory) of a non abelian free group must be a free factor. The pr…
Some lower bounds on Shelah rank in the free group
Javier de la Nuez González, Chloé Perin, Rizos Sklinos
We give some lower bounds on the Shelah rank of varieties in the free group whose coordinate groups are hyperbolic towers.
Forking and JSJ decompositions in the free group II
Chloé Perin, Rizos Sklinos
We give a complete characterization of the forking independence relation over any set of parameters in the free groups of finite rank, in terms of the decompositions relative…
On the (non) superstable part of the free group
Chloé Perin, Rizos Sklinos
In this short note we prove that a definable set over is superstable only if .
Forking and JSJ decompositions in the free group
Chloé Perin, Rizos Sklinos
We give a description of the model theoretic relation of forking independence in terms of the notion of JSJ decompositions in non abelian free groups.
On groups and fields interpretable in torsion-free hyperbolic groups
Chloé Perin, Anand Pillay, Rizos Sklinos +1
We prove that the generic type of a non-cyclic torsion-free hyperbolic group G is foreign to any interpretable abelian group, hence also to any interpretable field. This result dep…
Hyperbolic towers and independent generic sets in the theory of free groups
Larsen Louder, Chloé Perin, Rizos Sklinos
We use hyperbolic towers to answer some model theoretic questions around the generic type in the theory of free groups. We show that all the finitely generated models of this theor…
Homogeneity in the free group
Chloé Perin, Rizos Sklinos
We show that any non abelian free group $\F$ is strongly -homogeneous, i.e. that finite tuples of elements which satisfy the same first-order properties are in the same o…
Elementary embeddings in torsion-free hyperbolic groups
Chloé Perin
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 hyper…