 Quine atom

A Quine atom is a set whose sole member is itself. It violates the Axiom of foundation while respecting the axiom of extensionality. Swapping pairwise distinct old objects $a_n$ with their singletons in a Rieger-Bernays permutation model supplies many Quine atoms, provided those transpositions have disjoint supports. For example, the old ordinals $a_n=\omega +n$ and their singletons are disjoint families.