 Under its ordinary English interpretation, this formula says that the set-theoretic universe doesn't contain any bijections between the natural numbers and x. In particular,  Ω(mˆ)  says that there is no bijection between the natural numbers and  mˆ.  In contrast, the model theoretic interpretation of  Ω(mˆ)—the  one which is relevant to the fact that M  ⊨ Ω[mˆ]—says  only that the domain of M doesn't contain any bijections between the natural numbers and  mˆ.[23]  Clearly, these two interpretations have the potential to come apart. 