>>12611322What works for countable sets might not work for uncountables . With the axiom of choice you can do all sorts of weird things like construct non-measurable sets of the Banach-Tarsky paradox.
What axioms you chose to apply regarding which of the possible undefinable subsets of reals exist (such as non-measurable ones) and which don't have no bearing on concrete mathematical statements such as the twin prime conjecture or the Riemann hypothesis. So I wouldn't worry about the higher infinities too much.
