Aczel's anti-foundation axiom

Aczel's anti-foundation axiom is an alternative to the standard foundation axiom in set theory, which states that every non-empty set must contain an element that is disjoint from itself. The foundation axiom helps to avoid certain paradoxes and ensures that sets are constructed in a well-defined manner, typically preventing sets from containing themselves directly or indirectly. Aczel's anti-foundation axiom, on the other hand, allows for the existence of "non-well-founded" sets.