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Automorphism groups of randomized structures | | Tomás Ibarlucía
; | | Date: |
2 May 2016 | | Abstract: | 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 the separable
models of the theory of beautiful pairs of randomizations, and we show that
this theory is in general not $aleph_0$-categorical. | | Source: | arXiv, 1605.0473 | | Services: | Forum | Review | PDF | Favorites | |
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