[FOM] Platonism and Formalism

[Robert M. Solovay]

On Wed, 10 Sep 2003, Harvey Friedman wrote:
>
> Some relevant background is as follows.
>
> 1) there apparently is no mathematical logician willing to assert that they
> are convinced that
>
> #) ZF + "there exists a nontrivial elementary embedding from some V(kappa)
> into V(kappa), where kappa is an inaccessible cardinal"
>
> is consistent;
>
> 2) nor do any think that there are good grounds for believing it. Nor have
> any put forward plans for gathering evidence about it;
>

	Harvey,

	Have you asked Hugh Woodin what he thinks about # ? Back when I
was doing set-theory we talked about principles which might well be much
stronger than even the variant of # where "inacessible" is replaced by
"inaccessible limit of inaccessibles". I admit that I never asked him if
he believed the principles in question were consistent. Of course, they
certainly aren't **true** by well-known results of Kunen. {So I presume
the "it" that is discussed in 2) is the consistency of # rather than #
itself.}

	--Bob Solovay