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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 $\RR$.
- Results about ordered classes can be found here.
- 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