  It's important to emphasize that Skolem's own notion of relativity is more sophisticated than this. Let's grant that the specific element which serves as “the empty set” will not remain constant as we move from one model of set theory to another—with the empty set in the first model becoming, perhaps, a singleton in the second. Nonetheless, we can still use a formula in the language of set theory to capture the notion “x is the empty set” in an essentially absolute way. In any model of our axioms, an element mˆ ∈  M will satisfy the open formula “∀y y ∉ x” if and only if the set {m | M  ⊨  m ∈ mˆ }  is really empty. Hence, there's at least a sense in which we can still capture the notion “x is the empty set” from within the algebraic framework. And this point extends more widely—a similar argument would apply to notions like “x is a singleton” or “x has seventeen members.” Even on the algebraic conception of axiomatization, therefore, there are some set-theoretic notions which we can still pin down pretty precisely. What the Löwenheim-Skolem theorems show is that, no matter how rich our (first-order) set-theoretic axioms may be, we cannot use this kind of technique to pin down the notion “x is uncountable.” This is the result which lies behind all of Skolem's talk about “relativity,” and it's a result which highlights a genuine weakness in the algebraic approach to set-theoretic  axiomatization.[34]