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arXiv · 1602.02429

A note on the Akemann-Doner and Farah-Wofsey constructions

Tristan Bice·Piotr Koszmider
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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 $\aleph_1$ 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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Tristan Bice, Piotr Koszmider. 2016-02-07. A note on the Akemann-Doner and Farah-Wofsey constructions. https://doi.org/10.1090/proc/13242

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