  For our purposes, the second step in this argument has already been considered in enough detail in the context of our discussion of Skolem; so we'll simply recap the main points here. On the algebraic conception of set theory, basic set-theoretic notions are characterized by looking at the model theory of first-order axiomatizations of set theory. Notions which remain fixed as we move from model to model—in the sense of “fixed” that we discussed in the last section—have an “absolute” significance; notions which vary as we move from model to model have only a “relative” significance. Given this, the Löwenheim-Skolem theorems show that the notions of countability and uncountability will in fact vary as we move from model to model. On the algebraic conception of set theory, therefore, these notions are only  “relative.”[36]