FOM: large cardinals and P vs NP

[Ralf-Dieter Schindler]

On Thu, 2 Aug 2001, Stephen Cook wrote:

> I suppose that a large cardinal axiom could be consistent with ZFC,
> but in some sense still false.  But in this case, could it imply
> a false statement of number theory?

Such an axiom couldn't be true in a transitive model of ZF. So in
some sense it can't have been a natural large cardinal axiom. We
expect the common large cardinal axioms to be realizable in
(transitive !) inner models of set theory, and there are many deep
results supporting this expectation.
--Ralf Schindler