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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II

[axiom for new sets by combination]

5 ideas
Zermelo introduced Pairing in 1930, and it seems fairly obvious [Zermelo, by Maddy]
Pairing: ∀x ∀y ∃z (x ∈ z ∧ y ∈ z) [Kunen]
Pairing (with Extensionality) guarantees an infinity of sets, just from a single element [Rosen]
Axiom of Pairing: for all sets x and y, there is a set z containing just x and y [George/Velleman]
Pairing: For any two sets there exists a set to which they both belong [Clegg]