• Corpus ID: 119234772

The Calkin algebra is $\aleph_1$-universal

@article{Farah2017TheCA,
  title={The Calkin algebra is \$\aleph\_1\$-universal},
  author={Ilijas Farah and Ilan Hirshberg and Alessandro Vignati},
  journal={arXiv: Operator Algebras},
  year={2017}
}
We discuss the existence of (injectively) universal C*-algebras and prove that all C*-algebras of density character $\aleph_1$ embed into the Calkin algebra, $Q(H)$. Together with other results, this shows that each of the following assertions is relatively consistent with ZFC: (i) $Q(H)$ is a $2^{\aleph_0}$-universal C*-algebra. (ii) There exists a $2^{\aleph_0}$-universal C*-algebra, but $Q(H)$ is not $2^{\aleph_0}$-universal. (iii) A $2^{\aleph_0}$-universal C*-algebra does not exist. We… 
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