Content deleted Content added
m Open access bot: doi added to citation with #oabot. |
→Buchholz's ψ: forgot the clause adding the Cantor normal form terms |
||
Line 243:
* Let <math>P(\alpha)</math> be the set of distinct terms in the Cantor normal form of <math>\alpha</math> (with each term of the form <math>\omega^\xi</math> for <math>\xi \in \mathsf{On}</math>, see [[Cantor normal form theorem]])
* <math>C^0_\nu(\alpha) = \Omega_\nu</math>
* <math>C^{n+1}_\nu(\alpha) = C^{n}_\nu(\alpha) \cup \{\gamma \mid P(\gamma) \subseteq C^{n}_\nu (\alpha) \} \cup \{\psi_\nu(\xi) \mid \xi \in \alpha \cap C^{n}_\nu(\alpha) \land \xi \in C_u(\xi) \land u \leq \omega \}</math>
* <math>C_\nu(\alpha) = \bigcup\limits_{n < \omega} C^n_\nu(\alpha)</math>
* <math>\psi_\nu(\alpha) = \min(\{\gamma \mid \gamma \notin C_\nu(\alpha)\})</math>
| |||