Still, given a set of axioms, statements will fall into one of three categories. 1) Provably True, 2) Provably False, 3) Undecideable Claims that a statement i

Still, given a set of axioms, statements will fall into one of three categories. 1) Provably True, 2) Provably False, 3) Undecideable Claims that a statement is in category 1 are fully verifiable (by providing the proof). The same goes with claims that a statement is in category 2.