Comment by Epa095

I just want to be a bit pedantic here (but this is logic after all...), and point out that in point 1 above you are talking about syntactical completeness, and not semantical completeness, which is the kind of completes Gödel proves in his first completeness proof. I think people are often confused because of this overloading of the word. And it is about sentences(a formula withouth free variables), not any well formed formula.