Definition:Strict Well-Ordering/Definition 2

Definition
Let $\struct {S, \prec}$ be a relational structure.

Then $\prec$ is a strict well-ordering of $S$ :


 * $\prec$ is a connected relation on $S$
 * $\prec$ is strictly well-founded on $S$.

That is, whenever $T$ is a non-empty subset of $S$, $T$ has a strictly minimal element under $\prec$.

Also see

 * Equivalence of Definitions of Strict Well-Ordering