Dear Peter,

On Mon, 15 Sep 2014, Koellner, Peter wrote:

Dear Sy,

You proposed “strong unreachability” as intrinsically justified on the

basis of the maximal iterative conception of set, writing: “It is

compelling that _unreachability (and strong unreachability) with

reflection is faithful to maximality but these criteria have not yet

been systematically investigated”.

No!

Nothing “intrinsic” comes out of this programme until the spectrum of mathematical criteria that in some way mirror maximality have been studied, compared, unified and shown consistent. When I say “compellingly faithful to maximality” I do *not* mean “intrinsically justified”! I just mean that they should be regarded as criteria worth exploring when studying the different ways that maximality can be formulated mathematically, that is all.

At the end of your mail you raise the valid “bifurcation” issue. I cannot say with confidence that this won’t happen. It is too early to make a judgment on that.

Best,

Sy