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Preprint Number 2146
2146. Alexander Berenstein, C. Ward Henson and Tomás Ibarlucía Existentially closed measure-preserving actions of free groups E-mail: Submission date: 18March 2022 Abstract:
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 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 𝔽_k on its
profinite
completion with the Haar measure is metrically generic and therefore, as we
show, it is existentially closed. Mathematics Subject Classification: Keywords and phrases: |
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