Logic for metric structures and the number of universal sofic and hyperlinear groups
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- by Martino Lupini PDF
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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.References
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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
- MR Author ID: 1071243
- Email: mlupini@mathstat.yorku.ca
- 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
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 3238439