To my understanding, the Continuum Hypothesis cannot be proven true or false under ZFC. But to me this is very ambiguous as to the actual provability of CH.
Does this mean that even with infinite attempts, no person or computer could ever define a set that disproves the Continuum Hypothesis? Do we know if that is even possible?
If we do not know, do we know if it is possible to prove whether or not we can know? How much do we know about what we can know about this problem?
I am not trying to ask strictly as an answer to that hypothetical. I am asking in order to understand more about what it specifically meant by the -non-provability of the Continuum Hypothesis.