Back Axioma del conjunt buit Catalan Zermelo-Fraenkel-Mengenlehre#Die Axiome von ZF und ZFC German Αξίωμα του κενού συνόλου Greek Aksiomo de malplena aro Esperanto Axioma del conjunto vacío Spanish اصل موضوع مجموعه تهی Persian Axiome de l'ensemble vide French Aksiom praznog skupa Croatian Դատարկ բազմության աքսիոմ Armenian Assioma dell'insieme vuoto Italian
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.
- ^ a b Bagaria, 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
:3was 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.