Definition:Strictly Well-Ordered Set
Jump to navigation
Jump to search
Definition
Definition 1
Let $\struct {S, \RR}$ be a strictly totally ordered set.
Then $\struct {S, \RR}$ is a strictly well-ordered set if and only if $\RR$ is a strictly well-founded relation.
Definition 2
Let $\struct {S, \RR}$ be a relational structure.
Let $\RR$ be a strict well-ordering on $S$.
Then $\struct {S, \RR}$ is a strictly well-ordered set.