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THE UNIVERSAL THEORY OF THE HYPERFINITE II$_1$ FACTOR IS NOT COMPUTABLE

Published online by Cambridge University Press:  16 February 2024

ISAAC GOLDBRING  and
BRADD HART
ISAAC GOLDBRING
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF CALIFORNIA IRVINE, 340 ROWLAND HALL (BLDG.# 400), IRVINE CA 92697-3875 USA E-mail: isaac@math.uci.edu URL: http://www.math.uci.edu/~isaac
BRADD HART
Affiliation:
DEPARTMENT OF MATHEMATICS AND STATISTICS MCMASTER UNIVERSITY 1280 MAIN STREET HAMILTON, ON L8S 4K1 CANADA E-mail: hartb@mcmaster.ca URL: http://ms.mcmaster.ca/~bradd/
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Abstract

We show that the universal theory of the hyperfinite II$_1$ factor is not computable. The proof uses the recent result that MIP*=RE. Combined with an earlier observation of the authors, this yields a proof that the Connes Embedding Problem has a negative solution that avoids the equivalences with Kirchberg’s QWEP Conjecture and Tsirelson’s Problem.

Keywords

Connes embedding problemhyperfinite II1 factorundecidable universal theory

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Type
Article
Information
Bulletin of Symbolic Logic , Volume 30 , Issue 2 , June 2024 , pp. 181 - 198
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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