Christopher Eagle: Model theory of abelian real rank zero C*-algebras

27 June 2014, 13:30–15:00

Fields institute, Room 210

Speaker: Christopher Eagle

Title: Model theory of abelian real rank zero C*-algebras

Abstract: We consider algebras of the form $C(X)$, where $X$ is a $0$-dimensional compact Hausdorff space, from the point of view of continuous model theory.  We characterize these algebras up to elementary equivalence in terms of invariants of the Boolean algebra $CL(X)$ of clopen subsets of $X$.  We also describe several saturation properties that $C(X)$ may have, and relate these to topological properties of $X$ and saturation of $CL(X)$.  We will discuss some consequences of saturation when we view $C(X)$ as a $C^*$-algebra.  All the necessary background on continuous logic will be provided. This is joint work with Alessandro Vignati.