Re: The incompleteness theorems, Sigma-1-completeness, induction, all that

["Rupert"]

Aatu Koskensilta wrote:
> In the thread "Provable in T" the incompleteness theorem and their exact
> requirements - Sigma-1-completeness in particular - have been the
> subject of much discussion.
>
> Tbe first incompleteness theorem is usually expressed something like the
> following
>
>   For any extension T of Robinson arithmetic we can effectively find a
>   sentence G_T, s.t. G_T is true and undecidable in T iff T is
>   (1-)consistent.
>

"If" surely, not "iff"?

To make it "iff", the condition would have to be that T does not prove
its own inconsistency, which is weaker than 1-consistency.