  To summarize, then, the upshot of this discussion is this: if we take a purely algebraic approach to the axioms of set theory, then many basic set-theoretic notions—including the notions of countability and uncountability—will turn out to be relative. In Skolem's words: “axiomatizing set theory leads to a relativity of set-theoretic notions, and this relativity is inseparably bound up with every thoroughgoing axiomatization” (Skolem 1922, p. 296). Of course, this still leaves open the question of whether these notions are, as it were, absolutely relative—of whether there is some other, non-algebraic and non-thoroughgoing, way of understanding our axioms which does not lead to the sort of relativity we've just been discussing. It's when we turn to this latter question that the various interpretations of Skolem's paper begin to come apart.