# Re: A

Date: 11 Jul 2005 10:41:27 -0700

Message-ID: <1121103687.775746.129230_at_z14g2000cwz.googlegroups.com>

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 - 19:41:27 CEST