FOM: theory-edge mailing list

[Ralf-Dieter Schindler]

On Mon, 30 Jul 2001 JoeShipman at aol.com wrote:

> In my opinion P?=NP is unlikely to be independent of ZFC or related
> to large cardinals, but I would not be surprised if it was independent
> of Peano arithmetic.

It would be great if P?=NP were independent of ZF or would even have
anything to do with large cardinals; but there is no indication
whatsoever why this should be true. Easily, P=NP (or its negation)
cannot imply the existence of transitive models with large cardinals; as a
matter of fact, the construction of such models is *the* standard tool
for showing that natural math statements (rather than consistency
assertions) have a strength larger than ZF. I therefore wonder how Doria
(or anybody else, for this matter) might support the claim that large
cardinals are related to a natural arithmetical statement (like P=NP).
I guess revolutionary new methods would be called for.
--Ralf Schindler