Hi Folks, I was wondering if someone would be kind enough to explain the differences in the above theorems in as simple terms as possible. I've been reading various sites but I'm just getting more and more confused!

My understanding is the the completeness theorem follows on from Russell and Whitehead's Principa Mathematica and states that any formal system that is robust enough to axiomatize arithmetic must have statements that are true but not provable. (I couldn't find any examples of this so if anyone has one....)

BUT I can't see the difference between the above and in the incompleteness theorem.

Any help greatly appreciated. Thanks.

Dave.