Locally universal C*-algebras with computable presentations

03/04/2023

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by   Alec Fox, et al.

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The Kirchberg Embedding Problem (KEP) asks if every C*-algebra embeds into an ultrapower of the Cuntz algebra 𝒪_2. In an effort to provide a negative solution to the KEP and motivated by the recent refutation of the Connes Embedding Problem, we establish two computability-theoretic consequences of a positive solution to KEP. Both of our results follow from the a priori weaker assumption that there exists a locally universal C*-algebra with a computable presentation.