Logic for metric structures and the number of universal sofic and hyperlinear groups

Abstract

Using the model theory of metric structures, I give an alternative proof of the following result by Thomas: If the Continuum Hypothesis fails then there are power of the continuum many universal sofic groups up to isomorphism. This method is also applicable to universal hyperlinear groups, giving a positive answer to a question posed by Thomas.

14 pages; accepted for publication by the Proceedings of the American Mathematical Society

References in corpus (2)

• Almost commuting matrices with respect to normalized Hilbert-Schmidt norm
• Connes Embeddings and von Neumann Regular Closures of Group Algebras