Re: Columns without names

From: vc <boston103_at_hotmail.com>
Date: 20 Sep 2006 19:11:19 -0700
Message-ID: <1158804679.221207.35530@k70g2000cwa.googlegroups.com>

Marshall wrote:
> vc wrote:
> > paul c wrote:
> > > >
> > > > It depend on your favorite set theory. In some, R = {x | not( x in x)}
> > > > does not exist, in others it does.
> > > > ...
> > >
> > > I'm having a hard time seeing this - in what set theory would R = {x |
> > > not( x in x)} exist?
> >
> > NBG.

> Maybe I'm way off base here, but wouldn't the above not exist
> in any set theory with the Axiom of Regularity?

Axiom of regularity (foundation) does nothing to prevent R existence. Perhaps you meant axiom of separation.

> So it wouldn't
> be a set in ZF, either.

Sure it would not exist as anything in ZF thanks to AoS, but it would in NBG as a proper class.

>
>
> Marshall
Received on Wed Sep 20 2006 - 21:11:19 CDT