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arXiv:1111.0729 [math.LO]AbstractReferencesReviewsResources

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

Martino Lupini

Published 2011-11-03, updated 2014-05-24Version 3

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.

Comments: 14 pages; accepted for publication by the Proceedings of the American Mathematical Society
Categories: math.LO
Subjects: 03C20, 03E35, 20F69, 16E50
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