自作の順序数表記の構想メモ。定義は多分一生完成しない。
※関数記号に特に意味はありません。使われていないものを適当に選んでいます。
\({\rho}\)関数[]
ψ関数を拡張した順序数崩壊関数。
\({\rho^{\omega}_n}(0)={\rho^{n+1}_n}({\Omega_{n+1}})\)
\({\rho_1}({\Omega_2×{\alpha}})→{\Omega_{1+\alpha}}\)
- \({\rho}_0(0)={\psi}_0(0)\)
- \({\rho}_0({\Omega})={\psi}_0({\Omega})\)
- \({\rho}_0({\rho}_1(0))={\psi}_0({\psi}_1(0))\)
- \({\rho}_0({\rho}_1({\rho}_1({\Omega}_2)))={\psi}_0({\psi}_1({\Omega}_2))\)
- \({\rho}_0({\rho}_1({\rho}_1({\Omega}_2)+1))={\psi}_0({\psi}_1({\Omega}_2+1))\)
- \({\rho}_0({\rho}_1({\rho}_1({\Omega}_2)^{{\rho}_1({\Omega}_2)}))={\psi}_0({\psi}_1({\Omega}_2^{{\Omega}_2}))\)
- \({\rho}_0({\rho}_1({\rho}_1({\Omega}_2+1)))={\psi}_0({\psi}_1({\psi}_2(0)))\)
- \({\rho}_0({\rho}_1({\rho}_1({\Omega}_2×2)))={\psi}_0({\psi}_1({\psi}_2({\Omega}_3)))\)
- \({\rho}_0({\rho}_1({\rho}_1({\Omega}_2×2+{\rho}_1({\Omega}_2+{\rho}_1({\Omega}_2×2)))))={\psi}_0({\psi}_1({\psi}_2({\Omega}_3+{\psi}_2({\Omega}_3))))\)
- \({\rho}_0({\rho}_1({\rho}_1({\Omega}_2×2+{\rho}_1({\Omega}_2×2))))={\psi}_0({\psi}_1({\psi}_2({\Omega}_3×2)))\)
- \({\rho}_0({\rho}_1({\rho}_1({\Omega}_2×2+{\rho}_1({\Omega}_2×2+1))))={\psi}_0({\psi}_1({\psi}_2({\psi}_3(0))))\)
- \({\rho}_0({\rho}_1({\rho}_1({\Omega}_2×3)))={\psi}_0({\psi}_1({\psi}_2({\psi}_3({\Omega}_4))))\)
- \({\rho}_0({\rho}_1({\rho}_1({\Omega}_2×{\omega})))={\psi}_0({\Omega}_{\omega})\)
- \({\rho}_0({\rho}_1({\rho}_1({\Omega}_2×{\Omega})))={\psi}_0({\Omega}_{\Omega})\)
- \({\rho}_0({\rho}_1({\rho}_1({\Omega}_2^2)))={\psi}_0({\psi}_I(0))\)
- \({\rho_0}({\rho_1}({\rho_1}({\Omega_2^2×2})))={\psi_0({\psi_{I_2}(0)})}\)
- \({\rho}_0({\rho}_1({\rho}_1({\Omega}_2^3)))={\psi}_0({\psi}_{I(1,0)}(0))\)
- \({\rho}_0({\rho}_1({\rho}_1({\Omega}_2^{{\Omega}_2^{{\Omega}_2^{.^{.^.}}}})))={\rho_0({\rho}_1({\rho}_1({\rho}_2(0))))}\)
\({\tau}\)関数
\({\rho}\)関数の旧バージョンの簡略化。
- \({\tau_0}({\tau_0}({\Omega}))={\varepsilon_0}\)
- \({\tau_0}({\tau_0}({\Omega}),{\tau_0}({\Omega}))={\varepsilon_0×2}\)
- \({\tau_0}({\tau_0}({\Omega},0))={\varepsilon_0×{\omega}}\)
- \({\tau_0}({\tau_0}({\Omega},{\tau_0}({\tau_0}({\Omega}))))={\varepsilon_0^2}\)
- \({\tau_0}({\tau_0}({\Omega},{\tau_0}({\tau_0}({\Omega}),{\tau_0}({\tau_0}({\Omega})))))={\varepsilon_0^{\varepsilon_0}}\)
- \({\tau_0}({\tau_0}({\Omega},{\tau_0}({\Omega})))={\varepsilon_1}\)
- \({\tau_0}({\tau_0}({\Omega},{\tau_0}({\Omega},0)))={\psi_0({\omega})}\)
- \({\tau_0}({\tau_0}({\Omega},{\tau_0}({\Omega},{\tau_0}({\tau_0}({\Omega})))))={\psi_0({\psi_0(0)})}\)
- \({\tau_0}({\tau_0}({\Omega},{\tau_0}({\Omega},{\tau_0}({\Omega}))))={\psi_0({\Omega})}\)
- \({\tau_0}({\tau_0}({\Omega},{\tau_0}({\Omega},{\tau_0}({\Omega})),{\tau_0}({\Omega})))={\psi_0({\Omega+1})}\)
- \({\tau_0}({\tau_0}({\Omega},{\tau_0}({\Omega},{\tau_0}({\Omega})),{\tau_0}({\Omega},{\tau_0}({\Omega}))))={\psi_0({\Omega×2})}\)
- \({\tau_0}({\tau_0}({\Omega},{\tau_0}({\Omega},{\tau_0}({\Omega}),{\tau_0}({\Omega}))))={\psi_0({\Omega^2})}\)
- \({\tau_0}({\tau_0}({\Omega},{\tau_0}({\Omega},{\tau_0}({\Omega},0))))={\psi_0({\Omega^{\omega}})}\)
- \({\tau_0}({\tau_0}({\Omega},{\tau_0}({\Omega},{\tau_0}({\Omega},{\tau_0}({\Omega})))))={\psi_0({\Omega^{\Omega}})}\)
- \({\tau_0}({\tau_0}({\Omega},{\Omega}))={\psi_0({\psi_1(0)})}\)
- \({\tau_0}({\tau_0}({\Omega},{\Omega},{\tau_0}({\Omega})))={\psi_0({\psi_1(0)+1})}\)
- \({\tau_0}({\tau_0}({\Omega},{\Omega},{\tau_0}({\Omega},{\tau_0}({\Omega},{\Omega}))))={\psi_0({\psi_1(0)×2})}\)
- \({\tau_0}({\tau_0}({\Omega},{\Omega},{\tau_0}({\Omega},{\tau_0}({\Omega},{\Omega}),{\tau_0}({\Omega}))))={\psi_0({\psi_1(0)×{\Omega}})}\)
- \({\tau_0}({\tau_0}({\Omega},{\Omega},{\tau_0}({\Omega},{\tau_0}({\Omega},{\Omega}),{\tau_0}({\Omega},{\Omega}))))={\psi_0({\psi_1(0)^2})}\)
- \({\tau_0}({\tau_0}({\Omega},{\Omega},{\tau_0}({\Omega},{\tau_0}({\Omega},{\Omega},{\tau_0}({\Omega},{\tau_0}({\Omega},{\Omega}))))))={\psi_0({\psi_1(0)^{\psi_1(0)}})}\)
- \({\tau_0}({\tau_0}({\Omega},{\Omega},{\tau_0}({\Omega},{\Omega})))={\psi_0({\psi_1(1)})}\)
- \({\tau_0}({\tau_0}({\Omega},{\Omega},{\tau_0}({\Omega},{\Omega},0)))={\psi_0({\psi_1({\omega})})}\)
- \({\tau_0}({\tau_0}({\Omega},{\Omega},{\tau_0}({\Omega},{\Omega},{\tau_0}({\Omega},{\Omega}))))={\psi_0({\psi_1({\Omega_2})})}\)
- \({\tau_0}({\tau_0}({\Omega},{\Omega},{\tau_0}({\Omega},{\Omega},{\tau_0}({\Omega},{\Omega},{\tau_0}({\Omega},{\Omega})))))={\psi_0({\psi_1({\Omega_2^{\Omega_2}})})}\)
- \({\tau_0}({\tau_0}({\Omega},{\Omega},{\Omega}))={\psi_0({\psi_1({\psi_2(0)})})}\)
- \({\tau_0}({\tau_0}({\tau_1}(0)))={\psi_0({\Omega_{\omega}})}\)
- \({\tau_0}({\tau_0}({\tau_1}(0),{\Omega}))={\psi_0({\psi_{\omega}(0)})}\)
- \({\tau_0}({\tau_0}({\tau_1}(1)))={\psi_0({\Omega_{\omega^2}})}\)
- \({\tau_0}({\tau_0}({\tau_1}({\tau_0}({\Omega}))))={\psi_0({\Omega_{\Omega}})}\)
- \({\tau_0}({\tau_0}({\tau_1}({\Omega})))={\psi_0({\psi_I(0)})}\)
- \({\tau_0}({\tau_0}({\tau_1}({\Omega})),{\tau_0}({\tau_1}({\Omega})))={\psi_0({\psi_I(0)×2})}\)
- \({\tau_0}({\tau_0}({\tau_1}({\Omega}),{\tau_0}({\tau_1}({\tau_0}({\tau_1}({\Omega}))),{\Omega})))={\psi_0({\psi_{\psi_I(0)+1}(0)})}\)
- \({\tau_0}({\tau_0}({\tau_1}({\Omega}),{\tau_0}({\tau_1}({\Omega}))))={\psi_0({\psi_I(1)})}\)
- \({\tau_0}({\tau_0}({\tau_1}({\Omega}),{\tau_0}({\tau_1}({\Omega}),{\tau_0}({\tau_1}({\tau_0}({\tau_1}({\Omega})))))))={\psi_0({\psi_I({\psi_I(0)})})}\)
- \({\tau_0}({\tau_0}({\tau_1}({\Omega}),{\tau_0}({\tau_1}({\Omega}),{\tau_0}({\tau_1}({\Omega})))))={\psi_0({\psi_I(I)})}\)
- \({\tau_0}({\tau_0}({\tau_1}({\Omega}),{\tau_0}({\tau_1}({\Omega}),{\tau_0}({\tau_1}({\Omega}),{\tau_0}({\tau_1}({\Omega}))))))={\psi_0({\psi_I(I^I)})}\)
- \({\tau_0}({\tau_0}({\tau_1}({\Omega}),{\Omega}))={\psi_0({\psi_I({\psi_{I+1}(0)})})}\)
- \({\tau_0}({\tau_0}({\tau_1}({\Omega}),{\tau_1}({\tau_0}({\tau_1}({\tau_0}({\tau_1}({\Omega})))))))={\psi_0({\psi_I({\psi_{I+{\psi_I(0)}}(0)})})}\)
- \({\tau_0}({\tau_0}({\tau_1}({\Omega}),{\tau_1}({\tau_0}({\tau_1}({\Omega})))))={\psi_0({\psi_I({\psi_{I×2}(0)})})}\)
- \({\tau_0}({\tau_0}({\tau_1}({\Omega}),{\tau_1}({\Omega})))={\psi_0({\psi_I({\psi_{I_2}(0)})})}\)
- \({\tau_0}({\tau_0}({\tau_1}({\Omega},0)))={\psi_0({\psi_I({\psi_{I_{\omega}}(0)})})}\)
- \({\tau_0}({\tau_0}({\tau_1}({\Omega},{\Omega})))={\psi_0({\psi_{I(1,0)}(0)})}\)
- \({\tau_0}({\tau_0}({\tau_1}({\tau_1}({\tau_2}({\tau_2}(...))))))={\rho_0}({\rho_1}({\rho_1}({\rho_2}({\rho_2}({\rho_2}({\Omega_3×{\omega}}))))))\)
\({\beta}\)関数[]
- \({\beta_0}({\beta_0}({\Omega}))={\psi_0({\Omega^{\Omega}})}\)
- \({\beta_0}({\beta_0}({\Omega}),0,{\beta_0}({\Omega}))={\psi_0({\Omega^{\Omega}})×2}\)
- \({\beta_0}({\beta_0}({\Omega}),{\omega})={\beta_0}({\Omega^{\Omega}+1})\)
- \({\beta_0}({\beta_0}({\Omega}),{\beta_0}({\Omega}))={\psi_0({\Omega^{\Omega}+{\Omega^{\psi_0({\Omega^{\Omega}})}}})}\)
- \({\beta_0}({\beta_0}({\Omega},0,{\beta_0}({\Omega})))={\psi_0({\Omega^{\Omega}×2})}\)
- \({\beta_0}({\beta_0}({\Omega},0,{\beta_0}({\Omega}),1))={\psi_0({\Omega^{\Omega}×{\omega}})}\)
- \({\beta_0}({\beta_0}({\Omega},0,{\beta_0}({\Omega}),1,{\beta_0}({\Omega})))={\psi_0({\Omega^{\Omega+1}})}\)
- \({\beta_0}({\beta_0}({\Omega},0,{\beta_0}({\Omega}),2))={\psi_0({\Omega^{\Omega+{\omega}}})}\)
- \({\beta_0}({\beta_0}({\Omega},0,{\beta_0}({\Omega}),2,{\beta_0}({\Omega})))={\psi_0({\Omega^{\Omega×2}})}\)
- \({\beta_0}({\beta_0}({\Omega},0,{\beta_0}({\Omega}),3))={\psi_0({\Omega^{\Omega×{\omega}}})}\)
- \({\beta_0}({\beta_0}({\Omega},0,{\beta_0}({\Omega}),3,{\beta_0}({\Omega})))={\psi_0({\Omega^{\Omega^2}})}\)
- \({\beta_0}({\beta_0}({\Omega},0,{\beta_0}({\Omega}),4))={\psi_0({\Omega^{\Omega^{\omega}}})}\)
- \({\beta_0}({\beta_0}({\Omega},0,{\beta_0}({\Omega}),4,{\beta_0}({\Omega})))={\psi_0({\Omega^{\Omega^{\Omega}}})}\)
- \({\beta_0}({\beta_0}({\Omega},0,{\beta_0}({\Omega}),{\omega}))={\psi_0({\psi_1(0)})}\)
- \({\beta_0}({\beta_0}({\Omega},0,{\beta_0}({\Omega}),{\omega^2}))={\psi_0({\psi_1({\Omega_2})})}\)
- \({\beta_0}({\beta_0}({\Omega},0,{\beta_0}({\Omega}),{\beta_0}({\Omega})))={\psi_0({\psi_1({\Omega_2^{\Omega}})})}\)
- \({\beta_0}({\beta_0}({\Omega},0,{\beta_0}({\Omega},0)))={\psi_0({\psi_1({\Omega_2^{\Omega}×{\omega}})})}\)
- \({\beta_0}({\beta_0}({\Omega},0,{\beta_0}({\Omega},0),{\beta_0}({\Omega},0)))={\psi_0({\psi_1({\Omega_2^{\Omega}×{\omega^2}})})}\)
- \({\beta_0}({\beta_0}({\Omega},0,{\beta_0}({\Omega},0,{\beta_0}({\Omega}))))={\psi_0({\psi_1({\Omega_2^{\Omega}×{\Omega}})})}\)
- \({\beta_0}({\beta_0}({\Omega},0,{\beta_0}({\Omega},0,{\beta_0}({\Omega})),{\beta_0}({\Omega},0)))={\psi_0({\psi_1({\Omega_2^{\Omega}×{\Omega×{\omega}}})})}\)
- \({\beta_0}({\beta_0}({\Omega},0,{\beta_0}({\Omega},0,{\beta_0}({\Omega})),{\beta_0}({\Omega},0),{\beta_0}({\Omega},0,{\beta_0}({\Omega}))))={\psi_0({\psi_1({\Omega_2^{\Omega}×{\Omega^2}})})}\)
- \({\beta_0}({\beta_0}({\Omega},0,{\beta_0}({\Omega},0,{\beta_0}({\Omega})),{\beta_0}({\Omega},0,0)))={\psi_0({\psi_1({\Omega_2^{\Omega}×{\Omega^{\omega}}})})}\)
- \({\beta_0}({\beta_0}({\Omega},0,{\beta_0}({\Omega},0,{\beta_0}({\Omega})),{\beta_0}({\Omega},0,1,1)))={\psi_0({\psi_1({\Omega_2^{\Omega+1}})})}\)
- \({\beta_0}({\beta_0}({\Omega},0,{\beta_0}({\Omega},0,{\beta_0}({\Omega})),{\beta_0}({\Omega},0,1,1),{\beta_0}({\Omega},0,{\beta_0}({\Omega}))))={\psi_0({\psi_1({\Omega_2^{\Omega×2}})})}\)
- \({\beta_0}({\beta_0}({\Omega},0,{\beta_0}({\Omega},0,{\beta_0}({\Omega})),{\beta_0}({\Omega},0,1,1,0)))={\psi_0({\psi_1({\Omega_2^{\Omega×{\omega}}})})}\)
- \({\beta_0}({\beta_0}({\Omega},0,{\beta_0}({\Omega},0,{\beta_0}({\Omega})),{\beta_0}({\Omega},0,1,1,0),{\beta_0}({\Omega},0,{\beta_0}({\Omega}))))={\psi_0({\psi_1({\Omega_2^{\Omega^2}})})}\)
- \({\beta_0}({\beta_0}({\Omega},0,{\beta_0}({\Omega},0,{\beta_0}({\Omega})),{\beta_0}({\Omega},0,1,1,0,0)))={\psi_0({\psi_1({\Omega_2^{\Omega^{\omega}}})})}\)
- \({\beta_0}({\beta_0}({\Omega},0,{\beta_0}({\Omega},0,{\beta_0}({\Omega})),{\beta_0}({\Omega},0,1,1,0,0),{\beta_0}({\Omega},0,{\beta_0}({\Omega}))))={\psi_0({\psi_1({\Omega_2^{\Omega^{\Omega}}})})}\)
- \({\beta_0}({\psi_0}({\Omega},0,{\psi_0}({\Omega},0,{\beta_0}({\Omega})),{\beta_0}({\Omega},0,1,1,0,1)))={\psi_0({\psi_1({\Omega_2^{\psi_1(0)}})})}\)
- \({\beta_0}({\beta_0}({\Omega},0,{\beta_0}({\Omega},0,{\beta_0}({\Omega})),{\beta_0}({\Omega},0,{\beta_0}({\Omega}))))={\psi_0({\psi_1({\Omega_2^{\psi_1({\Omega_2^{\Omega}})}})})}\)
- \({\beta_0}({\beta_0}({\Omega},0,{\beta_0}({\Omega},0,{\beta_0}({\Omega}),0)))={\psi_0({\psi_1({\Omega_2^{\psi_1({\Omega_2^{\Omega}})×{\omega}}})})}\)
- \({\beta_0}({\beta_0}({\Omega},0,{\beta_0}({\Omega},0,{\beta_0}({\Omega}),0,{\beta_0}({\Omega}))))={\psi_0({\psi_1({\Omega_2^{\psi_1({\Omega_2^{\Omega}})×{\Omega}}})})}\)
- \({\beta_0}({\beta_0}({\Omega},0,{\beta_0}({\Omega},0,{\beta_0}({\Omega},0))))={\psi_0({\psi_1({\Omega_2^{\psi_1({\Omega_2^{\Omega}})^{\omega}}})})}\)
- \({\beta_0}({\beta_0}({\Omega},1))={\psi_0({\Omega_{\omega}})}\)
- \({\beta_0}({\beta_0}({\Omega},1,{\beta_0}({\Omega})))={\psi_0({\Omega_{\Omega}})}\)
- \({\beta_0}({\beta_0}({\Omega},1,{\Omega}))={\psi_0({\psi_I(0)})}\)
- \({\beta_0}({\beta_0}({\Omega},1,{\Omega},0,{\beta_0}({\Omega},1,{\Omega})))\)
- \(={\beta_0}({\beta_0}({\Omega},1,{\Omega},0,{\beta_0}({\Omega},1,{\beta_0}({\Omega},1,{\Omega},0,{\beta_0}({\Omega},1,{\beta_0}({\Omega},1,{\Omega},0,{\beta_0}({\Omega},1,...)))))))\)
- \({\beta_0}({\Omega},1,{\Omega},0,{\beta_0}({\Omega},1,{\beta_0}({\Omega},1,{\Omega}),0,{\Omega},1))={\psi_0({\Omega_{\psi_I(0)+{\omega}}})}\)
- \({\beta_0}({\beta_0}({\Omega},1,{\Omega},0,{\beta_0}({\Omega},1,{\beta_0}({\Omega},1,{\beta_0}({\Omega},1,{\Omega}),0,{\Omega},1))))={\psi_0({\Omega_{\Omega_{\psi_I(0)+{\omega}}}})}\)
- \({\beta_0}({\beta_0}({\Omega},1,{\Omega},0,{\beta_0}({\Omega},1,{\Omega})))={\psi_0({\psi_I(1)})}\)
- \({\beta_0}({\beta_0}({\Omega},1,{\beta_0},0,{\beta_0}({\Omega},1,{\Omega}),1))={\psi_0({\psi_I({\omega})})}\)
- \({\beta_0}({\beta_0}({\Omega},1,{\Omega},0,{\beta_0}({\Omega},1,{\Omega}),1,{\beta_0}({\Omega},1,{\beta_0}({\Omega},1,{\Omega}))))={\psi_0({\psi_I({\psi_I(0)})})}\)
- \({\beta_0}({\beta_0}({\Omega},1,{\Omega},0,{\beta_0}({\Omega},1,{\Omega}),1,{\beta_0}({\Omega},1,{\Omega})))={\psi_0({\psi_I(I)})}\)
- \({\beta_0}({\beta_0}({\Omega},1,{\Omega},0,{\beta_0}({\Omega},1,{\Omega}),2))={\psi_0({\psi_I(I^{\omega})})}\)
- \({\beta_0}({\beta_0}({\Omega},1,{\Omega},0,{\beta_0}({\Omega},1,{\Omega}),{\omega}))={\psi_0({\psi_I({\psi_{I+1}(0)})})}\)
- \({\beta_0}({\beta_0}({\Omega},1,{\Omega},0,{\Omega},1))={\psi_0({\psi_I({\Omega_{I+{\omega}}})})}\)
- \({\beta_0}({\beta_0}({\Omega},1,{\Omega},0,{\Omega},1,{\beta_0}({\Omega},1,{\beta_0}({\Omega},1,{\Omega}))))={\psi_0({\psi_I({\Omega_{I+{\psi_I(0)}}})})}\)
- \({\beta_0}({\beta_0}({\Omega},1,{\Omega},0,{\Omega},1,{\beta_0}({\Omega},1,{\Omega})))={\psi_0({\psi_I({\Omega_{I×2}})})}\)
- \({\beta_0}({\beta_0}({\Omega},1,{\Omega},0,{\Omega},1,{\Omega}))={\psi_0({\psi_I({\psi_{I_2}(0)})})}\)
- \({\beta_0}({\beta_0}({\Omega},1,{\Omega},1))={\psi_0({\psi_{I_{\omega}}(0)})}\)
- \({\beta_0}({\beta_0}({\Omega},1,{\Omega},1,{\beta_0}({\Omega},1,{\beta_0}({\Omega},1,{\Omega}))))={\psi_0({\psi_{I_{\psi_I(0)}}(0)})}\)
- \({\beta_0}({\beta_0}({\Omega},1,{\Omega},1,{\beta_0}({\Omega},1,{\Omega})))={\psi_0({\psi_{I_I}(0)})}\)
- \({\beta_0}({\beta_0}({\Omega},1,{\Omega},1,{\Omega}))={\psi_0({\psi_{I(1,0)}(0)})}={\tau_0}({\tau_0}({\tau_1}({\Omega},{\Omega})))\)
- \({\beta_0}({\beta_0}({\Omega},1,{\Omega},1,{\Omega},0,{\Omega}))={\tau_0}({\tau_0}({\tau_1}({\Omega},{\Omega}),{\Omega}))\)
- \({\beta_0}({\beta_0}({\Omega},1,{\Omega},1,{\Omega},0,{\Omega},1,{\Omega},1,{\Omega}))={\tau_0}({\tau_0}({\tau_1}({\Omega},{\Omega}),{\tau_1}({\Omega},{\Omega})))\)
- \({\beta_0}({\beta_0}({\Omega},1,{\Omega},1,{\Omega},1))={\tau_0}({\tau_0}({\tau_1}({\Omega},{\Omega},0)))\)
- \({\beta_0}({\beta_0}({\Omega},1,{\Omega},1,{\Omega},1,{\Omega}))={\tau_0}({\tau_0}({\tau_1}({\Omega},{\Omega},{\Omega})))\)
- \({\beta_0}({\beta_0}({\Omega},2))={\tau_0}({\tau_0}({\tau_1}({\tau_1}(0))))\)
- \({\beta_0}({\beta_0}({\Omega},2,0,{\Omega},2))={\tau_0}({\tau_0}({\tau_1}({\tau_1}(0)),{\tau_1}({\tau_1}(0))))\)
- \({\beta_0}({\beta_0}({\Omega},2,1))={\tau_0}({\tau_0}({\tau_1}({\tau_1}(0),0)))\)
- \({\beta_0}({\beta_0}({\Omega},2,1,{\Omega}))={\tau_0}({\tau_0}({\tau_1}({\tau_1}(0),{\Omega})))\)
- \({\beta_0}({\beta_0}({\Omega},2,2))={\tau_0}({\tau_0}({\tau_1}({\tau_1}(1))))\)
- \({\beta_0}({\beta_0}({\Omega},2,{\Omega}))={\tau_0}({\tau_0}({\tau_1}({\tau_1}({\Omega}))))\)
- \({\beta_0}({\beta_0}({\Omega},3))={\tau_0}({\tau_0}({\tau_1}({\tau_1}({\tau_1}(0)))))\)
- \({\beta_0}({\beta_0}({\Omega},{\omega}))={\tau_0}({\tau_0}({\tau_1}({\tau_1}({\Omega_2}))))\)
- \({\beta_0}({\beta_0}({\Omega},{\omega},0,{\Omega},{\omega}))={\tau_0}({\tau_0}({\tau_1}({\tau_1}({\Omega_2})),{\tau_1}({\tau_1}({\Omega_2}))))\)
- \({\beta_0}({\beta_0}({\Omega},{\omega},1))={\tau_0}({\tau_0}({\tau_1}({\tau_1}({\Omega_2}),0)))\)
- \({\beta_0}({\beta_0}({\Omega},{\omega},1,{\Omega},{\omega}))={\tau_0}({\tau_0}({\tau_1}({\tau_1}({\Omega_2}),{\tau_1}({\Omega_2}))))\)
- \({\beta_0}({\beta_0}({\Omega},{\omega},2))={\tau_0}({\tau_0}({\tau_1}({\tau_1}({\Omega_2},0))))\)
- \({\beta_0}({\beta_0}({\Omega},{\omega},{\omega}))={\tau_0}({\tau_0}({\tau_1}({\tau_1}({\Omega_2},{\tau_1}({\Omega_2})))))\)
- \({\beta_0}({\beta_0}({\Omega},{\omega},{\omega+1}))={\tau_0}({\tau_0}({\tau_1}({\tau_1}({\Omega_2},{\tau_1}({\Omega_2},0)))))\)
- \({\beta_0}({\beta_0}({\Omega},{\omega},{\Omega}))={\tau_0}({\tau_0}({\tau_1}({\tau_1}({\Omega_2},{\tau_1}({\Omega_2},{\Omega})))))\)
- \({\beta_0}({\beta_0}({\Omega},{\omega},{\Omega},{\omega}))={\tau_0}({\tau_0}({\tau_1}({\tau_1}({\Omega_2},{\tau_1}({\Omega_2},{\Omega}),{\tau_1}({\Omega_2})))))\)
- \({\beta_0}({\beta_0}({\Omega},{\omega},{\Omega},{\omega},{\Omega}))={\tau_0}({\tau_0}({\tau_1}({\tau_1}({\Omega_2},{\tau_1}({\Omega_2},{\Omega}),{\tau_1}({\Omega_2},{\Omega})))))\)
- \({\beta_0}({\beta_0}({\Omega},{\omega+1}))={\tau_0}({\tau_0}({\tau_1}({\tau_1}({\Omega_2},{\tau_1}({\Omega_2},{\Omega},0)))))\)
- \({\beta_0}({\beta_0}({\Omega},{\omega+1},{\omega},{\Omega},{\omega+1}))={\tau_0}({\tau_0}({\tau_1}({\tau_1}({\Omega_2},{\tau_1}({\Omega_2},{\Omega},0),{\tau_1}({\Omega_2},{\Omega},0)))))\)
- \({\beta_0}({\beta_0}({\Omega},{\omega+1},{\omega+1}))={\tau_0}({\tau_0}({\tau_1}({\tau_1}({\Omega_2},{\tau_1}({\Omega_2},{\Omega},0,0)))))\)
- \({\beta_0}({\beta_0}({\Omega},{\omega+1},{\Omega}))={\tau_0}({\tau_0}({\tau_1}({\tau_1}({\Omega_2},{\tau_1}({\Omega_2},{\Omega},{\Omega})))))\)
- \({\beta_0}({\beta_0}({\Omega},{\omega+2}))={\tau_0}({\tau_0}({\tau_1}({\tau_1}({\Omega_2},{\tau_1}({\Omega_2},{\tau_1}(0))))))\)
- \({\beta_0}({\beta_0}({\Omega},{\omega×2}))={\tau_0}({\tau_0}({\tau_1}({\tau_1}({\Omega_2},{\tau_1}({\Omega_2},{\tau_1}({\tau_1}({\Omega_2})))))))\)
- \({\beta_0}({\beta_0}({\Omega},{\omega^2}))={\tau_0}({\tau_0}({\tau_1}({\tau_1}({\Omega_2},{\tau_1}({\Omega_2},{\tau_1}({\Omega_2}))))))\)
- \({\beta_0}({\beta_0}({\Omega},{\omega^{\omega}}))={\tau_0}({\tau_0}({\tau_1}({\tau_1}({\Omega_2},{\tau_1}({\Omega_2},{\tau_1}({\Omega_2},0))))))\)
- \({\beta_0}({\beta_0}({\Omega},{\Omega}))={\tau_0}({\tau_0}({\tau_1}({\tau_1}({\Omega_2},{\tau_1}({\Omega_2},{\tau_1}({\Omega_2},{\tau_1}({\Omega_2})))))))\)
多変数\({\psi}\)関数[]
stage function?
- \({\psi_0(1,0)}={\omega}\)
- \({\psi_0(1,1)}={\Omega}\)
- \({\psi_0(1,{\psi_0(1,0)})}={\Omega_{\omega}}\)
- \({\psi_{\psi_0(1,{\Omega(1,0)})}(0)}={\Omega_{\Omega_{\Omega_{._{._.}}}}}={\psi_I(0)}\)
- \({\psi_0(1,{\Omega(1,0)})}=I\)
- \({\psi_0(1,{\Omega(1,0)+1})}={\Omega_{I+1}}\)
- \({\psi_0(1,{\Omega(1,0)+{\psi_0(1,{\Omega(1,0)})}})}={\Omega_{I×2}}\)
- \({\psi_0(1,{\Omega(1,0)+{\psi_0(1,{\Omega(1,0)+1})}})}={\Omega_{\Omega_{I+1}}}\)
- \({\psi_{\psi_0(1,{\Omega(1,0)×2})}(0)}={\Omega_{\Omega_{._{._{._{I+1}}}}}}={\psi_{I_2}}(0)\)
- \({\psi_0(1,{\Omega(1,0)×2})}=I_2\)
- \({\psi_0(1,{\Omega(1,0)×{\omega}})}=I_{\omega}\)
- \({\psi_0(1,{\Omega(1,0)×{\psi_0(1,{\Omega(1,0)})}})}=I_I\)
- \({\psi_{\psi_0(1,{\Omega(1,0)^2})}(0)}=I_{I_{I_{._{._.}}}}\)
\({\nu}\)関数[]
\({\rho_{\omega}}\)関数
- \({\nu_0}({\nu_0({\Omega})})={\psi_0({\Omega})}\)
- \({\nu_0({\nu_0({\Omega})+1})}={\psi_0({\Omega}+1)}\)
- \({\nu_0({\nu_0({\Omega})}+{\nu_0({\nu_0({\Omega})}+1)})}={\psi_0({\Omega}+{\psi_0({\Omega+1})})}\)
- \({\nu_0({\nu_0({\nu_0({\Omega})}+1)})}={\psi_0({\psi_1(0)})}\)
- \({\nu_0({\nu_0({\nu_0({\Omega})}+1)}+{\nu_0({\nu_0({\nu_0({\Omega})})}+1)})}={\psi_0({\psi_1(0)+{\psi_0({\Omega}+1)}})}\)
- \({\nu_0({\nu_0({\nu_0({\Omega})}×2)})}={\rho_0({\rho_1({\rho_1({\Omega_2})})})}\)
- \({\nu_0({\nu_0({\nu_0({\Omega})}×3)})}={\rho_0({\rho_1({\rho_1({\Omega_2}×2)})})}\)
- \({\nu_0({\nu_0({\nu_0({\nu_0({\Omega})+1})})})}={\rho_0({\rho_1({\rho_1({\rho_2(0)})})})}\)
- \({\nu_0({\nu_0({\Omega+1})})}={\rho_0({\Omega_{\omega}})}\)