Definition:Minimally Superinductive Class

Definition

Let $A$ be a class.

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

Then $A$ is minimally superinductive under $g$ if and only if:

$A$ is superinductive under $g$

no proper subclass of $A$ is superinductive under $g$.

Also see

• Definition:Superinductive Class

• Definition:Inductive Class under General Mapping
• Definition:Minimally Inductive Class under General Mapping

• Results about minimally superinductive classes can be found here.

Sources

• 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $4$: Superinduction, Well Ordering and Choice: Part $\text I$ -- Superinduction and Well Ordering: $\S 2$ Superinduction and double superinduction