  In effect, this analysis treats Skolem's paradox as a straightforward case of equivocation. There's one interpretation of  Ω(mˆ)  under which this formula really does entail that  mˆ  is an uncountable set; there's another—quite different—interpretation which ensures that M  ⊨ Ω[mˆ];  Skolem's Paradox depends on confusing these two interpretations. In principle, we should be no more surprised to find that this confusion leads us astray then we are to find that our direct deposits aren't buried in the local riverbank. Indeed the model-theoretic case may be a bit worse than the banking case: you could get lucky and find buried treasure while digging in the riverbank, but it's a straightforward theorem that if M is countable, then {m | M  ⊨  m ∈  mˆ }  is also countable.