Authors: Eagle, Christopher James
Farah, Ilijas 
Kirchberg, Eberhard
Vignati, Alessandro
Title: Quantifier elimination in C*-algebras
Journal: International Mathematics Research Notices
Volume: 2017
Issue: 24
First page: 7580
Last page: 7606
Issue Date: 1-Dec-2017
Rank: M21
ISSN: 1073-7928
DOI: 10.1093/imrn/rnw236
Abstract: 
The only unital C∗-algebras that admit elimination of quantifiers in continuous logic in the language of unital C∗-algebras are C, C2, C(Cantor space) and M2(C). We also prove that the theory of C∗-algebras does not have model companion and show that the theory of Mn(On+1) is not ∀∃-axiomatizable for any n ≥ 2.
Publisher: Oxford University Press

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