Meanings
- mathematicsThe axiom that the power set of any set exists and is a valid set, which appears in the standard axiomatisation of set theory, ZFC.
2012, A. H. Lightstone, H. B. Enderton (editor), Mathematical Logic: An Introduction to Model Theory, Plenum Press, Softcover, page 292, The Axiom of Power Set asserts that the collection of all subsets of a set is a set. […] Adding the Axiom of Power Set compels the collection empty to be a set.
3 more examples
The axiom of choice differs from other axioms of ZF by stating existence of a set (i.e., a choice function) without defining it (unlike, for instance, the axiom of pairing or the axiom of power set).
1978, Thomas Jech, Set Theory, Academic Press, page 38Verifying that the axiom of power set is in #92;#123;#92;phi#92;in#92;mathcal#123;L#125;#42;#58;S#92;vdash#92;mathcal#123;I#125;(#92;phi)#92;#125; relies on some rudimentary comprehension axioms.
2003, Thomas Forster, Reasoning About Theoretical Entities, World Scientific, page 51But the ZF axioms of which the hierarchy is an intuitive model involve impredicative quantifications. Most striking is the axiom of power set in tandem with the axiom of separation.
2011, Adam Rieger, “9: Paradox, ZF, and the Axiom of Foundation”, in David DeVidi, Michael Hallett, Peter Clark, editors, Logic, Mathematics, Philosophy: Vintage Enthusiasms: Essays in Honour of John L. Bell, Springer, page 183Synonyms: power set axiom
Synonyms & antonyms
proper nounThe axiom that the power set of any set exists and is a valid set, which appears in the standard axiomatisation of set theory, ZFC.
Translations
Finnish potenssijoukkoaksiooma
- potenssijoukkoaksioomaaxiom of set theory
Italian assioma dell'insieme potenza
- assioma dell'insieme potenzaaxiom of set theory
Cite this entry
axiom of power set. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/axiom%20of%20power%20set
“axiom of power set.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/axiom%20of%20power%20set. Accessed November 5, 2026.
WatkinsX Dictionary, s.v. “axiom of power set,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/axiom%20of%20power%20set.
Source: axiom of power set on Wiktionary, CC BY-SA 4.0.