Single Idea 13033

[catalogued under 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / d. Axiom of Unions III]

Full Idea

Axiom of Union: ∀F ∃A ∀Y ∀x (x ∈ Y ∧ Y ∈ F → x ∈ A). That is, the union of a set (all the members of the members of the set) must also be a set.

Clarification

The 'F' is in a Gothic font in Kunen; it represents a 'family' of sets

Gist of Idea

Union: ∀F ∃A ∀Y ∀x (x ∈ Y ∧ Y ∈ F → x ∈ A)

Source

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

Book Reference

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