## Abstract

We discuss the existence of (injectively) universal C*-algebras and prove that all C*-algebras of density character ℵ_{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^{ℵ}_{0}-universal C*-algebra. (ii) There exists a 2^{ℵ}_{0}-universal C*-algebra, but Q(H) is not 2^{ℵ}_{0}-universal, (iii) A 2^{ℵ}_{0}-universal C*-algebra does not exist. We also prove that it is relatively consistent with ZFC that (iv) there is no ℵ_{1}-universal nuclear C*-algebra, and that (v) there is no ℵ_{1}-universal simple nuclear C*-algebra.

Original language | English |
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Pages (from-to) | 287-309 |

Number of pages | 23 |

Journal | Israel Journal of Mathematics |

Volume | 237 |

Issue number | 1 |

DOIs | |

State | Published - 1 Mar 2020 |

## ASJC Scopus subject areas

- Mathematics (all)

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