[FOM] Query Concerning Excluded Middle & CH

Colin McLarty colin.mclarty at case.edu
Fri Jan 25 16:50:45 EST 2013

I can confirm there are examples.  I believe it is Nik Weaver who has
explained this situation best to me.


On Fri, Jan 25, 2013 at 9:39 AM, John Burgess <jburgess at princeton.edu> wrote:
> There has been at least one theorem in number theory proved by showing that
> it follows from the Riemann hypothesis AND that it follows from the negation
> of the Riemann hypothesis, and then appealing to excluded middle. (See
> Ireland & Rosen, _A Classical Introduction to Modern Number Theory_ ,
> Theorem 20.6.1.) My highly fallible memory tells me  that 35 years or so
> ago, as a post-doc in Madison, I was told by some authority that there was a
> similar example in analysis involving CH. Can anyone confirm this --- I
> mean, confirm that there is such an example, and not confirm that I was told
> there was --- and provide a reference? (Further examples from number theory
> involving RH would also be welcome.)
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