[FOM] CH and mathematics
John Baldwin
jbaldwin at uic.edu
Wed Feb 6 09:22:59 EST 2008
Nik,
Can you tell us what OCA is? In Faraj's paper he refers to another paper
for the statement?
On Tue, 5 Feb 2008, Nik Weaver wrote:
>
> 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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John T. Baldwin
Director, Office of Mathematics Education
Department of Mathematics, Statistics,
and Computer Science M/C 249
jbaldwin at uic.edu
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