User:Dfeuer/Minimally Inductive under Mapping

Definition
Let $A$ be a class.

Let $g$ be a mapping whose domain includes $A$ as a subclass.

Then $A$ is minimally inductive under $g$, or minimally $g$-inductive, iff:


 * $A$ is User:Dfeuer/Definition:Inductive under Mapping under $g$.


 * No proper subclass of $A$ is inductive under $g$. That is, if $B \subseteq A$ and $B$ is inductive under $g$, then $B = A$.