Saturation and elementary equivalence of C*-algebras

Christopher J. Eagle; Alessandro Vignati

doi:10.1016/j.jfa.2015.04.013

Saturation and elementary equivalence of C*-algebras

Logic 2015-10-08 v4 Operator Algebras

Authors: Christopher J. Eagle , Alessandro Vignati

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Abstract

We study the saturation properties of several classes of $C^*$ -algebras. Saturation has been shown by Farah and Hart to unify the proofs of several properties of coronas of $\sigma$ -unital $C^*$ -algebras; we extend their results by showing that some coronas of non- $\sigma$ -unital $C^*$ -algebras are countably degree- $1$ saturated. We then relate saturation of the abelian $C^*$ -algebra $C(X)$ , where $X$ is $0$ -dimensional, to topological properties of $X$ , particularly the saturation of $CL(X)$ .

Keywords

c*-algebras saturation elementary equivalence coronas sigma-unital model theory topological properties

Cite

@article{arxiv.1406.4875,
  title  = {Saturation and elementary equivalence of C*-algebras},
  author = {Christopher J. Eagle and Alessandro Vignati},
  journal= {arXiv preprint arXiv:1406.4875},
  year   = {2015}
}

Comments

36 pages. Version 4 is rewritten for clarity in several places

Saturation and elementary equivalence of C*-algebras

Abstract

Keywords

Cite

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