Linked from

The 10 pages that link to Axiom of pairing, each with the reason it gives.

• Zermelo–Fraenkel set theoryRelated: It supplies basic finite sets from which larger constructions can proceed.

• Ernst ZermeloBroader topic: It is one of the basic set-construction rules in Zermelo’s axiomatization.

• Cumulative hierarchyRelated: Pairing illustrates how set formation produces objects at later levels.

• Axiom of extensionalityRelated: Extensionality makes the set supplied by pairing unique by its specified members.

• Axiom of unionRelated: Together with union, pairing can form a set containing the elements of two chosen sets.

• Axiom of FoundationRelated: Pairing supplies sets whose membership patterns Foundation also constrains.

• Axiom of infinityRelated: It helps construct successor sets from existing sets.

• Axiom schema of specificationRelated: It is another Zermelo–Fraenkel axiom governing which sets can be formed.

• Axiom schema of replacementRelated: Pairing is another basic ZF axiom, but unlike replacement it forms sets from a fixed finite collection.

• Element of a setRelated: It guarantees sets can be formed with specified elements.