Year: 2025
Type: article
Abstract: In this paper we study expansions of infinite dimensional Hilbert spaces with a unitary representation of a discrete countable group. When the group is finite, we prove the theory of the corresponding expansion, regardless if it is existentially closed, has quantifier elimination, is ℵ 0 -categorical, ℵ 0 -stable and SFB. On the other hand, when the group involved is countably infinite, the theory of the Hilbert space expanded by the representation of this group is ℵ 0 -categorical up to perturbations. Additionally, when the expansion is model complete, we prove that it is ℵ 0 -stable up to perturbations.
Source: Confluentes Mathematici
DOI: 10.5802/cml.99
Authors: Alexander Berenstein, Juan Perez
Institutions: Universidad de Los Andes, University of Mons
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4416718138