🚀 go-pugleaf

In article <1992Nov2.205433.21208@tamsun.tamu.edu> cmenzel@tamsun.tamu.edu (Chris Menzel) writes:
>In article <1992Nov2.040843.4524@CSD-NewsHost.Stanford.EDU> pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt) writes:
>>That it [Foundation Axiom] is self-evident to you now seems more
>>an accident of culture---your training---than of something inherent in
>>the notion of set....
>
>I think that's too strong if, like me, you were introduced to set
>theory via the iterative hierarchy.  If that's your picture of sets,
>then the axiom *is* self-evident, and well-foundedness *is* an
>inherent property of sets.  The question is rather whether the
>iterative hierarchy encompasses *all* the sets, or whether we've just
>been looking at a rather limited portion of the universe, as is the
>case if we take the universe to be nonwellfounded ala Aczel.

The iterative hierarchy is consistent with Z but not with ZF.
Replacement (F) says in effect that any construction you can iterate
yields a set.  Hence if the universe is an iterative hierarchy it is a
set.

Anyone brought up on the iterative hierarchy was told a lie.
-- 
Vaughan Pratt			Ain't no truth in logic, son.