Definition:Strict Well-Ordering/Definition 2

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

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

$\prec$ 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 $\prec$.

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