Zermelo's Well-Ordering Theorem/Also known as

Zermelo's Well-Ordering Theorem: Also known as
Zermelo's Well-Ordering Theorem is also known just as the well-ordering theorem.

Some sources omit the hyphen: (Zermelo's) well ordering theorem.

It is also known just as Zermelo's Theorem.

Under this name it can often be seen worded:


 * Every set of cardinals is well-ordered with respect to $\le$.

This is called by some authors the Trichotomy Problem.

It is also referred to as the well-ordering principle, but this causes confusion with the result that states that the natural numbers are well-ordered.