Minimally Inductive Class under Slowly Progressing Mapping is Nest
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Theorem
Let $M$ be a class.
Let $g: M \to M$ be a slowly progressing mapping on $M$.
Let $M$ be a minimally inductive class under $g$.
Then $M$ is a nest.
Proof 1
Minimally Inductive Class under Slowly Progressing Mapping is Nest/Proof 1
Proof 2
By definition, a slowly progressing mapping is indeed a progressing mapping.
The result then follows from Minimally Inductive Class under Progressing Mapping induces Nest.
Sources
- 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $3$: The Natural Numbers: $\S 9$ Supplement -- optional