  Suppose, then, that M is a countable transitive model of ZFC. This has two effects on the analysis of Skolem's Paradox given in the last section. First, it ensures that the model-theoretic and the ordinary English interpretations of Ω(x) agree on the interpretation of “∈”: for m1, m2 ∈ M,   M  ⊨ m1 ∈ m2 if and only if m1 really is a member of  m2.[21]  In this case, therefore, the explanation of Skolem's Paradox has to involve the interpretation of the quantifiers. Second, the fact that M is transitive ensures that M gets more than just membership right. In particular, if f and m live in the domain of M, then M  ⊨ “f : ω → m is a bijection” if and only if f really is a bijection between the natural numbers and  m.[22]