Definition:Continuation of Woset

Definition

Let $\left({S, \preccurlyeq}\right)$ be a woset.

Let $\left({T, \preccurlyeq}\right)$ be a set with an ordering such that:

$(1): \quad T$ is an initial segment of $S$

$(2): \quad$ The ordering of the elements of $T$ is the same as their ordering in $S$.

Then $S$ is a continuation of $T$.

Also see

• Extension of Relation: the same concept, but as applied to the general relation

Sources

• 1960: Paul R. Halmos: Naive Set Theory ... (previous) ... (next): $\S 17$: Well Ordering