From: scott@math.csuohio.edu (Brian M. Scott)
Newsgroups: sci.logic,sci.math,sci.philosophy.meta
Subject: Re: Unit sets
Date: Thu, 27 Nov 1997 03:40:33 GMT
On Wed, 26 Nov 1997 16:42:57 -0500, "David A. Lamb"
wrote:
[snip]
>BUT... my question for the forum is this: Was the axiom of foundation
>ever shown to be independent of the rest of ZFC, i.e. is the theory ZFC
>- {foundation} + {exists(non-well-founded set)} consistent if ZFC is
>consistent?
Yes. It's not even too difficult to show; for ZF and ZF- (i.e.,
ignoring the question of AC) it follows from Exercise 23 in Ch. IV of
Ken Kunen's _Set Theory_.
Brian M. Scott