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


Author: Martino Lupini
Journal: Proc. Amer. Math. Soc. 142 (2014), 3635-3648
MSC (2010): Primary 03C20, 03E35, 20F69; Secondary 16E50
DOI: https://doi.org/10.1090/S0002-9939-2014-12089-2
Published electronically: June 25, 2014
MathSciNet review: 3238439
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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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Additional Information

Martino Lupini
Affiliation: Department of Mathematics and Statistics, N520 Ross, York University, 4700 Keele Street, Toronto, Ontario M3J 1P3, Canada – and – Fields Institute for Research in Mathematical Sciences, 222 College Street, Toronto, Ontario M5T 3J1, Canada
Email: mlupini@mathstat.yorku.ca

DOI: https://doi.org/10.1090/S0002-9939-2014-12089-2
Keywords: Ultraproducts, sofic groups, hyperlinear groups, logic for metric structures
Received by editor(s): November 2, 2011
Received by editor(s) in revised form: September 2, 2012, and October 29, 2012
Published electronically: June 25, 2014
Additional Notes: The author’s research was supported by the York University Elia Scholars Program, the ESF Short Visit Grant No. 4154, the National University of Singapore and the John Templeton Foundation
Communicated by: Julia Knight
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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