Inductive set

Bourbaki also defines an inductive set to be a partially ordered set that satisfies the hypothesis of Zorn's lemma when nonempty.

In descriptive set theory, an inductive set of real numbers (or more generally, an inductive subset of a Polish space) is one that can be defined as the least fixed point of a monotone operation definable by a positive Σ_n formula, for some natural number n, together with a real parameter.