Andrew_Critch comments on Löb’s Lemma: an easier approach to Löb’s Theorem

[Andrew_Critch]

It’s true that the deduction theorem is not needed, as in the Wikipedia proof. I just like using the deduction theorem because I find it intuitive (assume $A$, prove $B$, then drop the assumption and conclude $A\to B$) and it removes the need for lots of parentheses everywhere.

I’ll add a note about the meaning of $⊢$ so folks don’t need to look it up, thanks for the feedback!

[philh]

Thanks, that makes sense. And the added explanation helps a lot, I can see the argument for going from $⊢A\to B$ to $A⊢B$ now:

• PA proves $A\to B$;

• So PA + $A$ certainly proves $A\to B$, since it can prove everything PA can;

• Also, PA + $A$ proves $A$;

• So we have $A⊢A\wedge (\neg A\vee B)$;

• Which in turn gives us $A⊢B$.