FOM: Goldbach's Conjecture

[wtait@ix.netcom.com]

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