  Turn, now, to the third step in the Skolemite argument. The mathematical theorem which underlies this third step is clear. Let φ(x) be a formula which is supposed to define a unique set—e.g., “x  is the power set of ω” or “x  is the set of real  numbers.”[38]  Then we can find a model M  ⊨ ZFC and an element m ∈ M such that M  ⊨ φ(m) and {m′ ∈ M  | M  ⊨ m′ ∈ m } is only countable. So, if we're willing to concede that all it takes to be, say, the power set of ω is to satisfy the relevant defining formula in some model of set theory, then we can make sense of the claim that at least one instance of the power set of ω is “really” countable. If we are willing make the further assumption that it only takes one bijection to one such instance of the power set of ω to render the power set itself “absolutely” countable, then we can understand the Skolemite's strong claim about absolute countability. Of course, neither of these two final moves follows in the strict sense from the algebraic conception of axiomatization; but they are both moves which a proponent of the algebraic conception might well find congenial.