[FOM] Collecting independence results

John Tucker J.V.Tucker at swansea.ac.uk
Wed Oct 6 04:11:59 EDT 2004

Dear Daniel,

Naimark's problem is certainly of interest to mathematicians: Let A be a 
C* algebra with only one irreducible representation up to unitary 
equivalence, is A isomorphic to some K(H), the C* algebra of compact 
operators on a complex Hilbert space.

Charles Akemann and Nik Weaver have a recent (2003) paper called 
"Consistency of a counter-example to Naimark's problem" that you might 
like to look at. It uses Jensen's Diamond Principle. The case of ZFC was 
not settled.

I have acquired preprint but do not know if it is published. Perhaps 
other colleagues in FOM could help?

John V Tucker

University of Wales Swansea


Daniel Ian Rosenbloom wrote:
> Dear FOMers,
> For my undergraduate thesis, I'm considering doing a project on
> independence results in set theory that have applications to other areas
> of mathematics.  To that end, I am searching for any such results that
> exist scattered across articles and would benefit from a more
> consolidated/general/modern/detailed exposition and/or results that are of
> great general interest to mathematicians.  So far, I'm looking at
> Whitehead's conjecture, Kaplansky's conjecture, and Shelah and Soifer's
> work on AC and chromatic numbers of the plane, but I want to find more.
> Would anyone have references to other results that I could use?  I'd
> greatly appreciate any help.
> Sincerely,
> Daniel Rosenbloom
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