Obstructions to countable saturation in corona algebras

TL;DR

This paper investigates the conditions under which corona algebras of abelian C*-algebras are countably saturated, revealing that only the corona of $C_0(bR)$ exhibits this property.

Contribution

It establishes a precise criterion for countable saturation in corona algebras of abelian C*-algebras, specifically characterizing when such coronas are countably saturated.

Findings

Corona of $C_0(bR)$ is countably saturated.

Corona of $C_0(bR^n)$ is not countably saturated for $n eq 1$.

Provides insight into the structure of corona algebras in relation to saturation properties.

Abstract

We study the extent of countable saturation for coronas of abelian C*-algebras. In particular, we show that the corona algebra of $C_0(\bbR^n)$ is countably saturated if and only if $n=1$.