> [!NOTE] **Axiom** (Unrestricted) > > Suppose that $S(x)$ is a property. Then there is a set $Y$ whose elements are exactly those $x$ for which $S(x)$ holds $\exists Y \forall x (S(x) \to x\in Y)$ # Properties A consequence of this axiom is [[Russell's Paradox|Russel's paradox]] which is that the set of sets which do not contain themselves exists (a contradiction).