Submission date: 26 November 2023

Abstract:

We provide an example of two elementarily equivalent countable ICC groups G and H such that G is amenable and H is not inner amenable. As a result, we provide the first example of elementarily equivalent groups whose group von Neumann algebras are not elementarily equivalent, answering a question asked by many researchers.

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Full text arXiv 2311.15409: pdf, ps.