AUTOMORPHISM GROUPS OF RANDOMIZED STRUCTURES
Copyright policy )AUTOMORPHISM GROUPS OF RANDOMIZED STRUCTURES
AbstractWe 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).
- University of Lyon System France
- UNIVERSITE JEAN MONNET SAINT-ETIENNE France
- Jean Monnet University France
- Institut Universitaire de France France
330, 03C30. Secondary: 22A15, Dynamical Systems (math.DS), randomization, 510, 03C45, FOS: Mathematics, Structure of topological semigroups, measurable wreath product, 22A05, Classification theory, stability, and related concepts in model theory, Mathematics - Dynamical Systems, \(\aleph_0\)-categorical, MSC: Primary: 22F50, Other model constructions, beautiful pairs, Model-theoretic algebra, Mathematics - Logic, Measurable group actions, $\aleph_0$-categorical, [MATH.MATH-LO]Mathematics [math]/Logic [math.LO], Structure of general topological groups, Groups as automorphisms of other structures, Roelcke precompact, 22F10, Logic (math.LO), Descriptive set theory
330, 03C30. Secondary: 22A15, Dynamical Systems (math.DS), randomization, 510, 03C45, FOS: Mathematics, Structure of topological semigroups, measurable wreath product, 22A05, Classification theory, stability, and related concepts in model theory, Mathematics - Dynamical Systems, \(\aleph_0\)-categorical, MSC: Primary: 22F50, Other model constructions, beautiful pairs, Model-theoretic algebra, Mathematics - Logic, Measurable group actions, $\aleph_0$-categorical, [MATH.MATH-LO]Mathematics [math]/Logic [math.LO], Structure of general topological groups, Groups as automorphisms of other structures, Roelcke precompact, 22F10, Logic (math.LO), Descriptive set theory
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