  Let's begin with Skolem's claim that axiomatizing set theory leads to a relativity of set-theoretic notions. One way to understand this claim is to view it against the backdrop of what we might call an algebraic or model-theoretic conception of axiomatization. On this conception, the axioms of set theory serve to characterize—or perhaps even to implicitly define—basic set-theoretic notions like set, membership and set-theoretic universe. So, a set-theoretic universe is simply a model for the axioms of set theory, a set is simply an element in some set-theoretic universe, and membership just refers to whatever binary relation a particular universe uses to interpret the symbol “∈.” On this conception of axiomatization, then, the axioms of set theory should not be seen as attempts at describing—or even partially describing—some antecedently given “intended model” of set theory; instead, the intended models of set theory are simply those models which happen to satisfy our initial collection of set-theoretic  axioms.[31]