TIDC#PROP. Transfinite Induction.
Let $C$ be a class of ordinals. Suppose:
- \[0\in C.\]
- \[\forall\alpha\in C : \alpha+1\in C.\]
For every limit ordinal $\alpha$,
\[\alpha\subseteq C \enspace\rimp\enspace \alpha\in C.\]Then $C=\Ord$.
TIDC#PROP. Transfinite Induction.
Let $C$ be a class of ordinals. Suppose:
- \[0\in C.\]
- \[\forall\alpha\in C : \alpha+1\in C.\]
For every limit ordinal $\alpha$,
\[\alpha\subseteq C \enspace\rimp\enspace \alpha\in C.\]Then $C=\Ord$.