  Now, should it turn out to be the case that the consistency sentences (and the other, related sentences discovered by Gödel in 1931) were the only instances of undecidable statements, then the sequence of systems in the above hierarchy would catch every problem that arises.  And although we would never have a single system that gave us a complete axiomatization of mathematical truth, we would have a series of systems that collectively covered the totality of mathematical truths.