Definition:Well-Orderable Set

Definition

Let $S$ be a set.

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

Class Theory

In the context of class theory, the definition follows the same lines:

Let $A$ be a class.

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

Also see

• Definition:Well-Ordering
• Definition:Well-Ordered Set