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

Authors: Tristan Bice and Piotr Koszmider
Journal: Proc. Amer. Math. Soc. 145 (2017), 681-687
MSC (2010): Primary 46L05, 03E75
Published electronically: August 30, 2016
MathSciNet review: 3577870
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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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Additional Information

Tristan Bice
Affiliation: Federal University of Bahia, Salvador, Brazil

Piotr Koszmider
Affiliation: Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00-656 Warszawa, Poland

Received by editor(s): February 7, 2016
Received by editor(s) in revised form: March 21, 2016, and April 3, 2016
Published electronically: August 30, 2016
Additional Notes: Part of the research leading to the results of this paper was conducted with support of the grant PVE Ciência sem Fronteiras - CNPq (406239/2013-4) while the first author was visiting the University of São Paulo in December 2015. The authors would like to thank Christina Brech for organizing the visit.
The first author was supported by an IMPA (Brazil) post-doctoral fellowship.
The second author was supported at the University of São Paulo by grant PVE Ciência sem Fronteiras - CNPq (406239/2013-4).
Communicated by: Adrian Ioana
Article copyright: © Copyright 2016 Retained by the authors

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