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

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

2011-11-03

arxiv.org/abs/1111.0729v1

Mathematics

Logic

15 pages; submitted to the Proceedings of the American Mathematical Society

Scientific paper

Simon Thomas gave an algebraic proof that, if the Continuum Hypothesis fails, then there are power of the continuum many universal sofic groups up to isomorphism, and asked if the same is true for universal hyperlinear groups. By means of model theory for metric structures, I give an alternative proof of Thomas' result, that entails the same result for universal hyperlinear groups, answering Thomas' question. As a direct consequence, I infer that the sequence of complex matrix algebras, regarded as ranked regular algebras, admits power of the continuum many ultraproducts under the failure of the Continuum Hypothesis, answering a question of G\'abor Elek.

Affiliated with

Also associated with

No associations

Rating

Logic for metric structures and the number of universal sofic and hyperlinear groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Logic for metric structures and the number of universal sofic and hyperlinear groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Logic for metric structures and the number of universal sofic and hyperlinear groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-701409