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In page Axiom of empty set:

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In axiomatic set theory, the axiom of empty set,[1][2] also called the axiom of null set[3] and the axiom of existence,[4][5] is a statement that asserts the existence of a set with no elements.[3] Although Zermelo originally stipulated the existence of a set with no elements as an axiom[6][7] , 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[citation needed] and the variant of general set theory that Burgess (2005) calls "ST,"[8] and a demonstrable truth in Zermelo–Fraenkel set theory, with or without the axiom of choice.[9]