  If M is not transitive, however, then nearly all of this falls apart. Bays has argued that there are versions of Skolem's Paradox which turn solely on the way certain non-transitive models interpret a few specific instances of the membership relation in Ω(x) (Bays 2007a, sections 4–5). Similar points would carry over to our discussion of power sets and real numbers in section 2.4. We can, for instance, find a countable model of ZFC which contains the whole set of real numbers as a member—the model remains countable only because  ℜ ≠  {m | M  ⊨  m ∈   ℜ} (Benacerraf 1985; Bays 2007a, section 1). In short, although the generic explanation of Skolem's Paradox that was given in section 2.2—the one which simply notices that there are some differences between the model-theoretic and the ordinary English interpretations of Ω(x) and then chalks Skolem's Paradox up to some kind of equivocation between these two interpretations—continues to hold up when we move to non-transitive models, the more-detailed analyses of 2.3–2.4 all break down. In the general non-transitive case, therefore, the analysis of section 2.2 may be the best we can do in giving an explanation of Skolem's Paradox (which is not to say that we can't give more-detailed explanations in the context of any particular non-transitive model).