PROP-TIDC. 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 $\alpha$,
\[\alpha\subseteq C \rimp \alpha\in C.\]Then $C=\Ord$.
PROP-TIDC. 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 $\alpha$,
\[\alpha\subseteq C \rimp \alpha\in C.\]Then $C=\Ord$.