Single Idea 13032

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

Full Idea

Axiom of Pairing: ∀x ∀y ∃z (x ∈ z ∧ y ∈ z). Any pair of entities must form a set.

Gist of Idea

Pairing: ∀x ∀y ∃z (x ∈ z ∧ y ∈ z)

Source

Kenneth Kunen (Set Theory [1980], §1.6)

Book Reference

Kunen,Kenneth: 'Set Theory: Introduction to Independence Proofs' [North-Holland 1980], p.12

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A Reaction

Repeated applications of this can build the hierarchy of sets.