Full Idea
The Trichotomy Principle (any number is less, equal to, or greater than, another number) turned out to be equivalent to the Axiom of Choice.
Gist of Idea
The Trichotomy Principle is equivalent to the Axiom of Choice
Source
Feferman / Feferman (Alfred Tarski: life and logic [2004], Int I)
Book Reference
Feferman,S/Feferman,A.B.: 'Alfred Tarski: life and logic' [CUP 2008], p.48
A Reaction
[He credits Sierpinski (1918) with this discovery]