Logic for metric structures and the number of universal sofic and hyperlinear groups
Logic
2016-05-06 v3
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.
Cite
@article{arxiv.1111.0729,
title = {Logic for metric structures and the number of universal sofic and hyperlinear groups},
author = {Martino Lupini},
journal= {arXiv preprint arXiv:1111.0729},
year = {2016}
}
Comments
14 pages; accepted for publication by the Proceedings of the American Mathematical Society