Definition:Well-Founded Ordered Set

Let $$\left({S; \preceq}\right)$$ be a poset.

Then $$\left({S; \preceq}\right)$$ is well-founded iff every non-empty subset of $$S$$ has a minimal element.

The term "well-founded" can equivalently be said to apply to the ordering $$\preceq$$ itself rather than to the poset as a whole.