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

Lupini, Martino

doi:10.1090/S0002-9939-2014-12089-2

Logic for metric structures and the number of universal sofic and hyperlinear groups
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Proc. Amer. Math. Soc. 142 (2014), 3635-3648 Request permission

Abstract:

Using the model theory of metric structures, the author gave an alternative proof of the following result by Thomas: If the Continuum Hypothesis fails, then there are $2^{2^{\aleph _{0}}}$ 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.

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