Editing Axiom of empty set (section)

{{Short description|Axiom of Set Theory}}
In [[axiomatic set theory]], the '''axiom of empty set''',<ref name=":0">{{Cite book |last=Cunningham |first=Daniel W. |title=Set theory: a first course |date=2016 |publisher=Cambridge University Press |isbn=978-1-107-12032-7 |series=Cambridge mathematical textbooks |location=New York, NY |pages=24}}</ref><ref name=":1">{{Cite web |title=Set Theory {{!}} Internet Encyclopedia of Philosophy |url=https://iep.utm.edu/set-theo/ |access-date=2024-06-10 |language=en-US}}</ref> also called the '''axiom of null set'''<ref name=":2">{{Citation |last=Bagaria |first=Joan |title=Set Theory |date=2023 |work=The Stanford Encyclopedia of Philosophy |editor-last=Zalta |editor-first=Edward N. |url=https://plato.stanford.edu/archives/spr2023/entries/set-theory/ |access-date=2024-06-10 |edition=Spring 2023 |publisher=Metaphysics Research Lab, Stanford University |editor2-last=Nodelman |editor2-first=Uri}}</ref> and the '''axiom of existence''',<ref>{{Cite book |last=Hrbacek |first=Karel |title=Introduction to set theory |last2=Jech |first2=Thomas J. |date=1999 |publisher=CRC Press |isbn=978-0-8247-7915-3 |edition=3. ed., rev. and expanded, [Repr.] |series=Pure and applied mathematics |location=Boca Raton, Fla. |pages=7}}</ref><ref name=":3" /> is a statement that asserts the existence of a set with no elements.<ref name=":2" /> 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 set theory]] and [[Zermelo–Fraenkel set theory]], with or without the [[axiom of choice]].<ref>{{Cite book |url=https://www.worldcat.org/oclc/50422939 |title=Set theory |last=Jech, Thomas J. |date=2003 |publisher=Springer |isbn=3-540-44085-2 |edition=The 3rd millennium ed., rev. and expanded |location=Berlin |pages=3 |language=en |oclc=50422939}}</ref>