Buchholz's psi-functions: Difference between revisions

Buchholz's psi-functions (edit)

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Line 7: * \(C_\nu^0(\alpha) = \Omega_\nu\) * \(C_\nu^{n+1}(\alpha) = C_\nu^n(\alpha) \cup \{\gamma + \delta, \~~psi_mu~~psi_\mu(\xi): \gamma, \delta, \xi \in C_\nu^n(\alpha) \land \xi < \alpha \land \xi \in C_\mu(\xi) \land \mu \leq \omega\}\) * \(C_\nu(\alpha) = \bigcup\{C_\nu^n(\alpha): n < \omega\}\) * \(\psi_\nu(\alpha) = \operatorname{mex}(C_\nu(\alpha))\), where \(\operatorname{mex}\) denotes minimal excludant. Line 17: * \(C_\nu^0(\alpha) = \Omega_\nu\) * \(C_\nu^{n+1}(\alpha) = C_\nu^n(\alpha) \cup \{\gamma + \delta, \~~psi_mu~~psi_\mu(\xi): \gamma, \delta, \mu, \xi \in C_\nu^n(\alpha) \land \xi < \alpha\}\) * \(C_\nu(\alpha) = \bigcup\{C_\nu^n(\alpha): n < \omega\}\) * \(\psi_\nu(\alpha) = \operatorname{mex}(C_\nu(\alpha))\), where \(\operatorname{mex}\) denotes minimal excludant.