Editing Axiom of regularity (section)

== Regularity in the presence of urelements ==

[[Urelements]] are objects that are not sets, but which can be elements of sets. In ZF set theory, there are no urelements, but in some other set theories such as [[Urelement#Urelements in set theory|ZFA]], there are. In these theories, the axiom of regularity must be modified. The statement "<math display="inline">x \neq \emptyset</math>" needs to be replaced with a statement that <math display="inline">x</math> is not empty and is not an urelement. One suitable replacement is <math display="inline">(\exists y)[y \in x]</math>, which states that ''x'' is [[inhabited set|inhabited]].