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Topic: Anti-foundation axiom
Replies: 11   Last Post: Mar 15, 2013 6:00 AM

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Frederick Williams

Posts: 2,164
Registered: 10/4/10
Re: Anti-foundation axiom
Posted: Mar 15, 2013 6:00 AM
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Nam Nguyen wrote:
> On 14/03/2013 1:14 PM, Shmuel (Seymour J.) Metz wrote:

> >
> > ZFC+(V=L) is not ZFC.

> Right. But there's also a sense that an Abelian group is a group.

I don't know why you write "there's also a sense", an Abelian group is a
group without doubt or qualification. But the theory of Abelian groups
is not the theory of groups. That is more analogous to Shmuel Metz's
ZFC+(V=L) is not ZFC. ZFC+(V=L) and ZFC are theories, not structures or
classes of structures.

When a true genius appears in the world, you may know him by
this sign, that the dunces are all in confederacy against him.
Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting

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