FOM: Tennant on set-theoretic and other foundations

[Martin Davis]

At 03:08 PM 2/24/98 -0500, JOE SHIPMAN, BLOOMBERG/  NEW YORK wrote:
>
>another example is the apparent necessity of analytic
>methods in number theory [are these always eliminable?]). -- Joe Shipman
>

According to the conservative extension result Sol Feferman has written
about (I'm not sure whether it's due to him or to him and Takeuti. Sol?)
arithmetic propositions provable using "ordinary" methods of analysis are
already provable in PA. Things like the prime number theorem are certainly
arithmetic.

Of course, we know by G\"odel that there are even \Pi_1 sentences of
arithmetic that require for their proof "analytic" methods. But then these
methods must go beyond the Feferman result.

Martin