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Hilbert spaces with generic groups of automorphisms
Archive for Mathematical Logic 46 (3-4):289-299 (2007)
Abstract
Let G be a countable group. We prove that there is a model companion for the theory of Hilbert spaces with a group G of automorphisms. We use a theorem of Hulanicki to show that G is amenable if and only if the structure induced by countable copies of the regular representation of G is existentially closedLinks
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Citations of this work
An approximate Herbrand’s theorem and definable functions in metric structures.Isaac Goldbring - 2012 - Mathematical Logic Quarterly 58 (3):208-216.
Continuous theory of operator expansions of finite dimensional Hilbert spaces and decidability.Aleksander Ivanov - forthcoming - Mathematical Logic Quarterly.
Unitary Representations of Locally Compact Groups as Metric Structures.Itaï Ben Yaacov & Isaac Goldbring - 2023 - Notre Dame Journal of Formal Logic 64 (2):159-172.
References found in this work
Simplicity in compact abstract theories.Itay Ben-Yaacov - 2003 - Journal of Mathematical Logic 3 (02):163-191.
Simple stable homogeneous expansions of Hilbert spaces.Alexander Berenstein & Steven Buechler - 2004 - Annals of Pure and Applied Logic 128 (1-3):75-101.
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