There are three different formulations of the continuum hypothesis—the interpolant version, the well-ordering version, and the surjection version. These versions are all equivalent to one another in ZFC but we shall be imposing a definability constraint and in this case there can be interesting differences (our discussion follows Martin (1976)). There is really a hierarchy of notions of definability—ranging up through the Borel hierarchy, the projective hierarchy, the hierarchy in L(ℝ), and, more generally, the hierarchy of universally Baire sets—and so each of these three general versions is really a hierarchy of versions, each corresponding to a given level of the hierarchy of definability (for a discussion of the hierarchy of definability see  §2.2.1 and  §4.6 of the entry   “Large Cardinals and Determinacy”). 