# Definition:Minimally Inductive Class under General Mapping/Definition 1

## Definition

Let $A$ be a class.

Let $g: A \to A$ be a mapping on $A$.

$A$ is minimally inductive under $g$ if and only if:

 $(1)$ $:$ $A$ is inductive under $g$ $(2)$ $:$ No proper subclass of $A$ is inductive under $g$.

## Also see

• Results about minimally inductive classes can be found here.