Single Idea 13462

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

Full Idea

It follows from the Axiom of Choice that every set can be well-ordered.

Gist of Idea

With the Axiom of Choice every set can be well-ordered

Source

William D. Hart (The Evolution of Logic [2010], 1)

Book Reference

Hart,W.D.: 'The Evolution of Logic' [CUP 2010], p.27


A Reaction

For 'well-ordered' see Idea 13460. Every set can be ordered with a least member.

Related Idea

Idea 13460 'Well-ordering' must have a least member, so it does the natural numbers but not the integers [Hart,WD]