Hal, Chaitin just says "you cannot prove 20 pound theorems with 10 pound axioms". But the infinite cascade of all provable theorems of number theory collectively does not convey more information than the axioms.
> But what if you declare theorems which say the same thing to be the > _same theorem_, rewritten? > Duraid Since a theorem is a symbol string, different strings cannot be the same theorem. Perhaps you mean you can easily derive certain theorems from others stating "the same thing, rewritten". But this is vague - you can derive all theorems from the axioms stating "the same thing, rewritten".
