[FOM] V = WF costs nothing

[Thomas Forster]

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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