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arXiv · 1111.0729

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

Martino Lupini
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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.

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Martino Lupini. 2011-11-03. Logic for metric structures and the number of universal sofic and hyperlinear groups. https://doi.org/10.1090/s0002-9939-2014-12089-2

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