[tombert]

ZFC Set Theory avoids Russell's paradox by having a few fundamental axioms that preclude it. It's actually mentioned in your wiki link in the `Set-theoretic responses` section.

ZFC is a bit messy sometimes, but it's actually kind of nice in its simplicity. I am a big fan of TLA+, for example, and it's really kind of beautiful how easily you can define incredibly precise invariants by using the set theory predicate logic.