I wouldn't say undecidable statements have no truth value. In any given model of set theory each statement is either true or false. If something is provable it

I wouldn't say undecidable statements have no truth value. In any given model of set theory each statement is either true or false. If something is provable it is true in every model, and if something is refutable it is false in every model. Undecidable statements can't be proved to be either true or false within a given proof system, but (1) in any given model are either true or false, as I said, and (2) can sometimes be shown to be true (or false) by arguments outside of the proof system considered.