Definition:Strict Well-Ordering/Definition 1

Definition

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 $S$.

Also see

• Equivalence of Definitions of Strict Well-Ordering

Sources

• 1971: Gaisi Takeuti and Wilson M. Zaring: Introduction to Axiomatic Set Theory: $\S 6.24$
• 1996: Winfried Just and Martin Weese: Discovering Modern Set Theory. I: The Basics ... (previous) ... (next): Part $1$: Not Entirely Naive Set Theory: Chapter $2$: Partial Order Relations