My apologies, I amuse myself too easily... On Fri, Oct 12, 2007 at 04:00:25PM -0500, Linas Vepstas wrote: > > not grounded on ZFC, mostly > cause its not constructivist. Non-concrete categories are, well, > roughly speaking bigger than the biggest infinities, and so ZFC doesn't > really address that.
One of my early confusions was that some older books use the words "does not exist" as a synonym for "proper class". Thus, to prove that something is a proper class, you prove that it "does not exist". For example, that it has more elements than any cardinal. Since each cardinal is infinitely more infinite than the last ... and there are infinitely more of them at each stage ... In fact, what was meant is that the class "does not exist as a set"; its bigger than any set could be. In particular, it cannot be grounded in ZFC. See, for example http://en.wikipedia.org/wiki/Proper_class http://en.wikipedia.org/wiki/New_Foundations http://en.wikipedia.org/wiki/Von_Neumann-Bernays-G%C3%B6del_axioms --linas ----- This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244&id_secret=53156770-b12b3e
