Re: what makes it true?

> Ittay Weiss wrote:
>
> > I don't know this theorem. I do know however the
> soundness theorem
> > that states that if a statement has a proof from a
> set of axioms
> > then it is true in any model where the axioms hold.
> Thus if something
> > can be proved it is true. I would appreciate it if
> you explain more
> > about this Goodstein theorem, or explain how can it
> be that what you
> > claim doesn't contradict the soundness theorem
>
> Better Google it up (just by: "Goodstein's Theorem")
> than asking *me*
> for an explanation.
>

according to what I found Goodstein's theorem asserts that a certain sequence is eventually zero. And further it was proved that this cannot be proved using PA. So this would be an example of a true statement which is not provale within PA. Certainly not the case of a statement which has a proof yet is false. As I said, according to the soundness theorem, this cannot happen (unless the system in inconsistent).

> Han de Bruijn
>
.

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