Quantifier elimination in C*-algebras

Abstract

The only C*-algebras that admit elimination of quantifiers in continuous logic are $\mathbb{C},{\mathbb{C}}^2$, $C($Cantor space$)$ and $M_2(\mathbb{C})$. We also prove that the theory of C*-algebras does not have model companion and show that the theory of $M_n({\mathcal{O}}_{n+1})$ is not $\forall \exists$-axiomatizable for any $n\ge 2$.

More improvements and bug fixes. To appear in IMRN

References in corpus (3)

• Invariant means and finite representation theory of C*-algebras
• Logic and operator algebras
• The pseudoarc is a co-existentially closed continuum

Cited by in corpus (2)

• The pseudoarc is a co-existentially closed continuum
• Expressive power of infinitary [0, 1]-valued logics