Definition:Minimally Inductive Class under General Mapping/Definition 1
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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 $g$|
|\((2)\)||$:$||No proper subclass of $A$ is inductive under $g$.|
- Results about minimally inductive classes can be found here.
- 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 $4.2$