The first formulation of CH is that there is no interpolant, that is, there is no infinite set A of real numbers such that the cardinality of A is strictly between that of the natural numbers and the real numbers. To obtain definable versions one simply asserts that there is no “definable” interpolant and this leads to a hierarchy of definable interpolant versions, depending on which notion of definability one employs. More precisely, for a given pointclass Γ in the hierarchy of definable sets of reals, the corresponding definable interpolant version of CH asserts that there is no interpolant in Γ. 