Single Idea 14444

[catalogued under 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX]

Full Idea

Zermelo has shown that [the Axiom of Choice] is equivalent to the proposition that every class is well-ordered, i.e. can be arranged in a series in which every sub-class has a first term (except, of course, the null class).

Gist of Idea

Choice is equivalent to the proposition that every class is well-ordered

Source

Bertrand Russell (Introduction to Mathematical Philosophy [1919], XII)

Book Reference

Russell,Bertrand: 'Introduction to Mathematical Philosophy' [George Allen and Unwin 1975], p.123


A Reaction

Russell calls Choice the 'Multiplicative' Axiom.