We present unified proofs of several properties of the corona of
$\sigma$-unital C*-algebras such as AA-CRISP, SAW*, being sub-$\sigma$-Stonean
in the sense of Kirchberg, and the conclusion of Kasparov's Technical Theorem.
Although our results were obtained by considering C*-algebras as models of the
logic for metric structures, the reader is not required to have any knowledge
of model theory of metric structures (or model theory, or logic in general).
The proofs involve analysis of the extent of model-theoretic saturation of
corona algebras.