[FOM] CH and mathematics
Nik Weaver
nweaver at math.wustl.edu
Tue Feb 5 13:03:40 EST 2008
Colin McLarty wrote:
> Compare Nik Weaver's current article:
>
> > http://arxiv.org/abs/math/0604198v1
>
> which James cites. The article says "it appears that C*-algebraists
> generally tend to regard a problem as solved when it has been answered
> using CH." I.e. they take the answer that follows from CH to be the
> right answer.
Yes, I think this is generally true. I should add, though, that
problems where CH has appeared tend to lie on the periphery of
the subject. I wouldn't want to leave the impression that set
theory is felt to be very relevant to mainstream C*-algebra ---
I don't think it is. Probably the central open problems in the
subject are all arithmetical.
My article was addressed to set theorists who might be stimulated
by these kinds of open independence problems. For example, see
Ilijas Farah's stunning use of OCA to prove that all automorphisms
of the Calkin algebra are inner:
http://front.math.ucdavis.edu/0705.3085
(Chris Phillips and I had previously shown that CH implies the
existence of outer automorphisms.)
Nik Weaver
Math Dept.
Washington University
St. Louis, MO 63130 USA
nweaver at math.wustl.edu
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