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Locally universal C*-algebras with computable presentations (2303.02301v1)
Published 4 Mar 2023 in math.LO, cs.CC, and math.OA
Abstract: The Kirchberg Embedding Problem (KEP) asks if every C*-algebra embeds into an ultrapower of the Cuntz algebra $\mathcal{O}_2$. 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.