Quantifier elimination in C*-algebras

Christopher J. Eagle; Ilijas Farah; Eberhard Kirchberg; Alessandro Vignati

Quantifier elimination in C*-algebras

Logic 2016-10-06 v5 Operator Algebras

Authors: Christopher J. Eagle , Ilijas Farah , Eberhard Kirchberg , Alessandro Vignati

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 $n\geq 2$ .

Keywords

c*-algebras

Cite

@article{arxiv.1502.00573,
  title  = {Quantifier elimination in C*-algebras},
  author = {Christopher J. Eagle and Ilijas Farah and Eberhard Kirchberg and Alessandro Vignati},
  journal= {arXiv preprint arXiv:1502.00573},
  year   = {2016}
}

Comments

More improvements and bug fixes. To appear in IMRN

Quantifier elimination in C*-algebras

Abstract

Keywords

Cite

Comments

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