Set Theory/Zermelo‒Fraenkel set theory

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Definition (Zermelo‒Fraenkel set theory):

Zermelo‒Fraenkel set theory is the theory given by the following axioms:

  1. Axiom of extensionality:
  2. Empty set:
  3. Pairing:
  4. Union:
  5. Power set:
  6. Regularity:
  7. Infinity:
  8. Comprehension: