Re: Implementable Set Theory and Consistency of ZFC

In article <2aed4$47283a1c$82a1e228$16577@xxxxxxxxxxxxxxxx>,
Han de Bruijn <Han.deBruijn@xxxxxxxxxxxxxx> wrote:

Jesse F. Hughes wrote:


There is, perhaps, a way in which your model is canonical. It seems
to me that it is a minimal model and, as you say, (5) is true in that
model. It simply does not follow that (1)-(4) entail (5).

And, as we have said, if (1)-(4) *did* entail (5), then so would
(1)-(4) + (X).

I don't agree. Infinity "adds" something to the system that makes it far
less transparent.

What particular property of appending infiniteness makes any of 5-8 any
less clear or less entailed than 1-4 do by themselves?
.