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AUTOMORPHISM GROUPS OF RANDOMIZED STRUCTURES

Published online by Cambridge University Press:  08 September 2017

TOMÁS IBARLUCÍA*
Affiliation:
UNIVERSITÉ DE LYON INSTITUT CAMILLE JORDAN 43 BLVD. DU 11 NOVEMBRE 1918 69622 VILLEURBANNE CEDEX FRANCE E-mail: ibarlucia@math.univ-lyon1.fr

Abstract

We study automorphism groups of randomizations of separable structures, with focus on the ℵ0-categorical case. We give a description of the automorphism group of the Borel randomization in terms of the group of the original structure. In the ℵ0-categorical context, this provides a new source of Roelcke precompact Polish groups, and we describe the associated Roelcke compactifications. This allows us also to recover and generalize preservation results of stable and NIP formulas previously established in the literature, via a Banach-theoretic translation. Finally, we study and classify the separable models of the theory of beautiful pairs of randomizations, showing in particular that this theory is never ℵ0-categorical (except in basic cases).

Type
Articles
Copyright
Copyright © The Association for Symbolic Logic 2017 

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