Axiom of empty set

In axiomatic set theory, the axiom of empty set, also called the axiom of null set and the axiom of existence, is a statement that asserts the existence of a set with no elements. Although Zermelo originally stipulated the existence of a set with no elements as an axiom , it can be treated as either an axiom or a derivable truth depending on the specific set-theoretic context. It is an axiom of Kripke–Platek set theory and the variant of general set theory that Burgess (2005) calls "ST," and a demonstrable truth in Zermelo–Fraenkel set theory, with or without the axiom of choice.