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] 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.[6]
^Cunningham, Daniel W. (2016). Set theory: a first course. Cambridge mathematical textbooks. New York, NY: Cambridge University Press. p. 24. ISBN 978-1-107-12032-7.
^"Set Theory | Internet Encyclopedia of Philosophy". Retrieved 2024-06-10.
^ abBagaria, Joan (2023), Zalta, Edward N.; Nodelman, Uri (eds.), "Set Theory", The Stanford Encyclopedia of Philosophy (Spring 2023 ed.), Metaphysics Research Lab, Stanford University, retrieved 2024-06-10
^Hrbacek, Karel; Jech, Thomas J. (1999). Introduction to set theory. Pure and applied mathematics (3. ed., rev. and expanded, [Repr.] ed.). Boca Raton, Fla.: CRC Press. p. 7. ISBN 978-0-8247-7915-3.
^Cite error: The named reference :3 was invoked but never defined (see the help page).
^Jech, Thomas J. (2003). Set theory (The 3rd millennium ed., rev. and expanded ed.). Berlin: Springer. p. 3. ISBN 3-540-44085-2. OCLC 50422939.
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