Inductive set
In descriptive set theory, an inductive set of real numbers is one that can be defined as the least fixed point of a monotone operation definable by a positive Σ1n formula, for some natural number n, together with a real parameter.
The inductive sets form a boldface pointclass; that is, they are closed under continuous preimages. In the Wadge hierarchy, they lie above the projective sets and below the sets in L. Assuming sufficient determinacy, the class of inductive sets has the scale property and thus the prewellordering property.
