  The analysis of sections 2.2–2.3 explains in general terms how a countable model can satisfy a formula like Ω(x) at a particular element. But it may still leave an obvious question unanswered: how can a countable model of ZFC satisfy such a formula? Granted that an arbitrary model can interpret a formula like Ω(x) in a peculiar manner—how can a model satisfy all of the axioms of set theory while still maintaining this peculiar interpretation? Shouldn't the fact that M satisfies ZFC ensure that M also gets basic set-theoretic notions like countable and uncountable correct?