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axiom of power set

axiom of power set proper noun: the axiom that the power set of any set exists and is a valid set, which appears in the standard axiomatisation of set theory, ZFC.

Proper noun

axiom of power set

  1. The axiom that the power set of any set exists and is a valid set, which appears in the standard axiomatisation of set theory, ZFC.
    • 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 38
    • Verifying 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 51
    Synonyms:
    power set axiom

Synonyms of axiom of power set

  • power set axiom

Questions about axiom of power set

What does axiom of power set mean?
Axiom of power set means the axiom that the power set of any set exists and is a valid set, which appears in the standard axiomatisation of set theory, ZFC.
What part of speech is axiom of power set?
Axiom of power set is a proper noun.

Words near axiom of power set in the dictionary

  1. axiom of choice
  2. axiom of countable choice
  3. axiom of extensionality
  4. axiom of infinity
  5. axiom of pairing
  6. axiom of power set
  7. axiom of regularity
  8. axiom of union
  9. axiom schema
  10. axiom schema of abstraction
  11. axiom schema of separation

Source and license

Adapted from Wiktionary: axiom of power set (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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