I know that there are statements that are neither provable nor disprovable within some set of axioms, and I also know that such statements are called undecidable. Please allow me to call these statements to be undecidable to the first order, or belong to $U_1$.
I was wondering if there is some kind of generalization of this concept. Are there any conjectures/statements of which we can prove that we cannot prove whether it is decidable or not? Such a statement would be undecidable to the second order, or belong to $U_2$. Generalizing even further:
What about statements that are in $U_\infty$ ?