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Topic: 10^7-ZFC
Replies: 15   Last Post: May 14, 2012 1:19 PM

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 Frederick Williams Posts: 2,166 Registered: 10/4/10
Re: 10^7-ZFC
Posted: May 13, 2012 9:57 AM

LudovicoVan wrote:

>
> Is it just sci-fi that we could build up a system step by step, adding an
> axiom/definition at a time, along with its closure, and checking the
> correctness of the resulting system at each step?

What is correctness, and how would you check it?

> If that is possible,
> wouldn't the resulting system always stay correct and, a fortiori,
> consistent?

Since NBG is finitely axiomatized, it has one axiom (i.e. the
conjunction of the usual axioms); also the definitions are just
notational conveniences which may be dispensed with. So by "adding an
axiom/definition at a time" you can have the whole of NBG immediately.
Can you prove, by your proposed method, that NBG is consistent?

--
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