Definition:Well-Orderable Set/Class Theory

Definition
Let $S$ be a set.

If it is possible to construct an ordering $\preceq$ on $S$ such that $\preceq$ is a well-ordering, then $S$ is defined as being well-orderable.

Also see
The Well-Ordering Theorem, which states that every set $S$ is well-orderable.

The Well-Ordering Theorem is Equivalent to the Axiom of Choice - assuming the truth of one, you can prove the other.

The Axiom of Choice, which states that every set of sets can have a choice function associated with it.