Definition:Minimally Inductive Class under General Mapping/Definition 2

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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 $g$             
\((2)\)   $:$   Every subclass of $A$ which is inductive under $g$ contains all the elements of $A$.             

Also see

  • Results about minimally inductive classes can be found here.