[FOM] Query Concerning Excluded Middle & CH

Epstein, Adam A.L.Epstein at warwick.ac.uk
Fri Jan 25 17:04:59 EST 2013

From: fom-bounces at cs.nyu.edu [fom-bounces at cs.nyu.edu] on behalf of John Burgess [jburgess at princeton.edu]
Sent: 25 January 2013 14:39
To: Foundations of Mathematics
Subject: [FOM] Query Concerning Excluded Middle & CH

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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