Definition:Totally Ordered Class

Definition
Let $V$ be a basic universe.

Let $\RR \subseteq V \times V$ be a relation.

Let $A$ be a subclass of the field of $\RR$.

Let the restriction of $\RR$ to $A$ be a total ordering on $A$.

Then $A$ is described as being totally ordered under $\RR$.

Also known as
A totally ordered class is also called a simply ordered class or linearly ordered class.