Definition:Well-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 well-ordering on $A$.

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

Also see

• Results about ordered classes can be found here.

Sources

• 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $4$: Superinduction, Well Ordering and Choice: Part $\text I$ -- Superinduction and Well Ordering: $\S 1$ Introduction to well ordering