Definition:Minimally Inductive Class under General Mapping/Definition 2

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

Also see

• Equivalence of Definitions of Minimally Inductive Class

• Results about minimally inductive classes can be found here.

Sources

• 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $3$: The Natural Numbers: $\S 4$ A double induction principle and its applications: Definition $4.2$