Yes, 'undecidable' is used for a similar class of mathematical problems. For example, the continuum hypothesis - another question about an equality of sets - is

Yes, 'undecidable' is used for a similar class of mathematical problems. For example, the continuum hypothesis - another question about an equality of sets - is undecidable in ZFC. This notion is strongly related to undecidability on Turing machines (possibly equivalent, depending on how you look at it).