期刊
JOURNAL OF SYMBOLIC LOGIC
卷 82, 期 3, 页码 1150-1179出版社
CAMBRIDGE UNIV PRESS
DOI: 10.1017/jsl.2017.2
关键词
randomization; measurable wreath product; aleph(0)-categorical; Roelcke precompact; beautiful pairs
类别
资金
- ECOS Nord exchange programme
- Agence Nationale de la Recherche project GruPoLoCo [ANR-11-JS01-0008]
- Agence Nationale de la Recherche (ANR) [ANR-11-JS01-0008] Funding Source: Agence Nationale de la Recherche (ANR)
We study automorphism groups of randomizations of separable structures, with focus on the aleph(0)-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 aleph(0)-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 aleph(0)-categorical (except in basic cases).
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