Existentially closed measure-preserving actions of free groups - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2022

Existentially closed measure-preserving actions of free groups

Résumé

This paper is motivated by the study of probability measure-preserving (pmp) actions of free groups using continuous model theory. Such an action is treated as a metric structure that consists of the measure algebra of the probability measure space expanded by a family of its automorphisms. We prove that the existentially closed pmp actions of a given free group form an elementary class, and therefore the theory of pmp $\mathbb{F}_k$-actions has a model companion. We show this model companion is stable and has quantifier elimination. We also prove that the action of $\mathbb{F}_k$ on its profinite completion with the Haar measure is metrically generic and therefore, as we show, it is existentially closed. We deduce our main result from a more general theorem, which gives a set of sufficient conditions for the existence of a model companion for the theory of $\mathbb{F}_k$-actions on a separably categorical, stable metric structure.

Dates et versions

hal-03635929 , version 1 (08-04-2022)

Identifiants

Citer

Alexander Berenstein, C. Ward Henson, Tomás Ibarlucía. Existentially closed measure-preserving actions of free groups. 2022. ⟨hal-03635929⟩
12 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More