Russell's paradox and axiom of separation I don't quite understand how the axiom of separation resolves Russell's paradox in an entirely satisfactory way (without relying on other axioms).
I see that it removes the immediate contradiction that is produced by unrestricted comprehension, but it seems that we still need further axioms to guarantee that a well-formed set $S$ will never contain the set of all given elements (of $S$) which do not contain themselves.
Is that correct? 

I don't think the axiom scheme of separation "resolves" Russell's paradox at all, but restricts the way of using predicates to determine sets.
The paradox is nothing but a proof that there is no one-to-one correspondence between predicates and classes: there are predicates that not defines a class. When writing sets as $\{x|p(x)\}$ that one-to-one correspondence is understood. Therefore axiomatic set theory is to show that sets exists and show rules how to create sets. If $A$ is a set, then the set $\{x\in A|p(x)\}$ never will cause any trouble, due to the theories.
