= Urelement
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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.
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