Definition:Strict Well-Ordering
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Definition
Definition 1
Let $\struct {S, \prec}$ be a relational structure such that $\prec$ is a strict total ordering.
Then $\prec$ is a strict well-ordering on $S$ if and only if $\prec$ is a strictly well-founded relation on $S$.
Definition 2
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 $S$.