A note on the Akemann-Doner and Farah-Wofsey constructions
Abstract
We remove the assumption of the continuum hypothesis from the Akemann-Doner construction of a non-separable C*-algebra A with only separable commutative C*-subalgebras. We also extend a result of Farah and Wofsey's, constructing 1 commuting projections in the Calkin algebra with no commutative lifting. This removes the assumption of the continuum hypothesis from a version of a result of Anderson. Both results are based on Luzin's almost disjoint family construction.
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