An urelement is an object permitted alongside sets, with no members, distinguished from the empty set by an atom or set predicate. Extensionality is restricted to sets, so distinct atoms need not be equal merely because they have no members. An atom is different from a Quine atom, which is a set with a self-member. In simple typed set theory with atoms, each sort may contain urelements in addition to the objects representing subsets of the preceding sort.
New to topics? Read the docs here!