  Taken together, these examples highlight a crucial fact: the “misinterpretations” which explained how a countable model can satisfy a sentence like  Ω(mˆ )  are actually fairly systematic. They also explain how these models can satisfy sentences like “R is the set of real numbers” or “Y is the power set of ω”; and they even explain how these models can satisfy the axioms of set theory (e.g., the power set axiom). When enough of these misinterpretations get put together, they jointly explain how it's possible for a countable model to both satisfy the axioms of set theory and, at the same time, maintain the peculiar interpretation of Ω(x) that we discussed in sections 2.2–2.3. In the end, then, while the Löwenheim-Skolem theorem may still be interesting technical fact—“a novel and unexpected feature of formal systems,” in van Heijenoort's words—Skolem's Paradox itself should no longer appear very paradoxical.