[FOM] V = WF costs nothing
T.Forster at dpmms.cam.ac.uk
Thu Feb 7 15:13:30 EST 2008
I think i see now what you are driving at. You are defending a thesis
to the effect that you lose no expressive power in restricting yourself
from ZF(C) to ZF(C) + V = WF. Agreed. Anything that you deny yourself
by working inside ZF(C) + V = WF you have already denied yourself by
working inside ZF(C).
You are quite right of course, and the theorems that bear this message
should be better known than they are.
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So perhaps i shouldn't quibble when you write:
In On Wed, 6 Feb 2008, Colin McLarty wrote:
> > The point is that there might be facts about
> > large collections that cannot be presented (``spun'')
> > as facts about wellfounded sets. Mightn't there?
> Well certainly yes. But none can concern the existence of
> mathematical structures up to isomorphism.
Why? Are you saying there are no big mathematical structures?
Isn't this the point at issue?
> > Church gave us a consistent set
> > theory which says there is a universal set.
> But this theory makes other changes as well. It restricts other
> means of set formation.
On the face of it, yes. But not *morally* as we say. One of the
axiom schemes is that the wellfounded sets are a model of ZF(C).
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