A NOTE ON THE AKEMANN-DONER AND FARAH-WOFSEY CONSTRUCTIONS.

Authors :: BICE, TRISTAN
KOSZMIDER, PIOTR
Source :: Proceedings of the American Mathematical Society; Feb2017, Vol. 145 Issue 2, p681-687, 7p
Publication Year :: 2017
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 N<subscript>1</subscript> 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. [ABSTRACT FROM AUTHOR]