> The solution to this paradox was to use a set of axioms (most commonly the Zermelo-Fraenkel axioms) which do not allow the construction of such a contradictor

> The solution to this paradox was to use a set of axioms (most commonly the Zermelo-Fraenkel axioms) which do not allow the construction of such a contradictory set ... Or one can adopt a non-well-founded set theory that admits such a set.