# FOM: Goldbach's Conjecture

wtait@ix.netcom.com wtait at ix.netcom.com
Sat Feb 28 08:49:55 EST 1998

Kanovei writes
>THEOREM (ZFC). If PA does not prove that the Goldbach Conjecture
>(GC) fails, then GC is true.
>
>ZFC can be replaced by Z, 2nd order arithmetic, perhaps even
>the topos theory, but I do not know whether we can start this:
>THEOREM (PA).
\phi \implies provable_PA(\phi') is a theorem of PA for any \Sigma_1
sentence \phi, including \\phi = not-GC.

Bill Tait

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