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|There is believed to be a mistake here, possibly a typo.|
In particular: Superinductive class does not assume that $g$ is the successor operation. I saw a few references to "superinductive with successor". Might we create a separate definition for that for ease and consistency of reference?
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Let $\alpha$ be a set.
$\alpha$ is an ordinal if and only if:
The class of all ordinals can be found denoted $\On$.
- $\Ord S$
whose meaning is:
- $S$ is an ordinal.
- 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $5$: Ordinal Numbers: $\S 1$ Ordinal numbers: Definition $1.1$