The Calkin algebra is not countably homogeneous

TL;DR

This paper demonstrates that the Calkin algebra and its unitary group's connected component lack countable homogeneity in continuous model theory, revealing limitations in their structural symmetry.

Contribution

It establishes the non-countable homogeneity of the Calkin algebra and its unitary group's connected component, a novel result in operator algebra model theory.

Findings

Calkin algebra is not countably homogeneous.

Connected component of the unitary group is not countably homogeneous.

Highlights limitations in the symmetry properties of these algebras.

Abstract

We show that the Calkin algebra is not countably homogeneous, in the sense of continuous model theory. We furthermore show that the connected component of the unitary group of the Calkin algebra is not countably homogeneous.