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Paul wrote:
> vc wrote:
> >>OK. but domains can be thought of as simply sets. So then the
> >>"collection of all domains" is like the "set of all sets" which, by
> >>Cantor's Paradox, isn't actually a well-defined set.
> >
> > In "naive" set theory, yes, in ZF, no. There is no problem with
> > defining a "set of all domains" provided that the set satisfies ZF
> > axioms.
>
> So couldn't our "set of all domains" be a valid domain itself? And thus
> a member of itself?
>
> Paul.
Not in ZF where, given D as a set of all domains formed at an earlier stage (see the "iterative/cumulative conception of set" I mentioned earlier in the thread), you can talk about D as being a member of some set formed at a later stage: {D,..} or {{D}, {D...}, ...} and so forth.
vc Received on Mon Jul 11 2005 - 12:41:27 CDT