Definition:Minimally Superinductive Class
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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: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