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Preprint Number 704
704. Isaac Goldbring and Thomas Sinclair
On Kirchberg's Embedding Problem
Submission date: 7 April 2014.
Kirchberg's Embedding Problem (KEP) asks whether every separable C^* algebra embeds into an ultrapower of the Cuntz algebra O_2. In this paper, we use model theory to show that this conjecture is equivalent to a local approximate nuclearity condition that we call the existence of good nuclear witnesses. In order to prove this result, we study general properties of existentially closed C^* algebras. The paper concludes with a discussion of the model theory of O_2. Several results in this last section are proven using some technical results concerning tubular embeddings, a notion first introduced by Jung for studying embeddings of tracial von Neumann algebras into the ultrapower of the hyperfinite II_1 factor.
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