structure for 'Formal Logic'    |     alphabetical list of themes    |     expand these ideas

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

[axiom for new sets from parts]

3 ideas
The Axiom of Union dates from 1899, and seems fairly obvious [Cantor, by Maddy]
Union: ∀F ∃A ∀Y ∀x (x ∈ Y ∧ Y ∈ F → x ∈ A) [Kunen]
Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg]