560 ページ

バシク行列の解析２ BMの名前の決定。

(0,0,0)(1,1,1)(2,2,2)以下の名前については次のようにします。

ファーストバックギア順序数(first back gear ordinal)
(0,0,0)(1,1,1)(2,2,0)

セカンドバックギア順序数(second back gear ordinal)
(0,0,0)(1,1,1)(2,2,1)(3,3,0)

オメガバック順序数(omega back ordinal)
(0,0,0)(1,1,1)(2,2,2)

(0,0,0)(1,1,1)(2,2,2)=ψ_Ω(χ(ω,0))?


バシク小行列数(活性関数は自乗)=WOBO(0,0,0)[3]

## 分析

\begin{array}{ll} (0)&=&\\ 1\\ \\ (0)(0)&=&\\ 2\\ \\ (0)(1)&=&\\ \omega\\ \\ (0)(1)(0)(1)&=&\\ \omega+\omega\\ \\ (0)(1)(1)&=&\\ \omega^2\\ \\ (0)(1)(2)&=&\\ \omega^\omega\\ \\ (0,0)(1,1)&=&\\ \epsilon_0\\ \\ (0,0)(1,1)(1,0)&=&\\ \epsilon_0\cdot\omega\\ \\ (0,0)(1,1)(1,0)(2,1)&=&\\ \epsilon_0^2\\ \\ (0,0)(1,1)(1,0)(2,1)(2,0)(3,1)&=&\\ \epsilon_0^{\epsilon_0}\\ \\ (0,0)(1,1)(1,0)(2,1)(2,0)(3,1)(2,0)&=&\\ \epsilon_0^{\epsilon_0\cdot \omega}\\ \\ (0,0)(1,1)(1,0)(2,1)(2,0)(3,1)(2,0)(3,1)&=&\\ \epsilon_0^{\epsilon_0^2}\\ \\ (0,0)(1,1)(1,0)(2,1)(2,0)(3,1)(3,0)&=&\\ \epsilon_0^{\epsilon_0^\omega}\\ \\ (0,0)(1,1)(1,0)(2,1)(2,0)(3,1)(3,0)(4,1)&=&\\ \epsilon_0^{\epsilon_0^{\epsilon_0}}\\ \\ (0,0)(1,1)(1,1)&=&\\ \epsilon_1\\ \\ (0,0)(1,1)(1,1)(1,1)&=&\\ \epsilon_2\\ \\ (0,0)(1,1)(2,0)&=&\\ \epsilon_\omega\\ \\ (0,0)(1,1)(2,0)(3,1)&=&\\ \epsilon_{\epsilon_0}\\ \\ (0,0)(1,1)(2,1)&=&\\ \zeta_0\\ \\ (0,0)(1,1)(2,1)(1,1)(2,0)(3,1)(4,1)&=&\\ \epsilon_{\zeta_0\cdot 2}\\ \\ (0,0)(1,1)(2,1)(1,1)(2,1)&=&\\ \zeta_1\\ \\ (0,0)(1,1)(2,1)(2,0)&=&\\ \zeta_\omega\\ \\ (0,0)(1,1)(2,1)(2,1)&=&\\ \phi_3(0)\\ \\ (0,0)(1,1)(2,1)(3,0)&=&\\ \phi_\omega(0)\\ \\ (0,0)(1,1)(2,1)(3,1)&=&\\ \Gamma_0\\ \\ (0,0)(1,1)(2,1)(3,1)(2,0)&=&\\ \psi_\Omega(\Omega^\Omega\cdot \omega)\\ \\ (0,0)(1,1)(2,1)(3,1)(2,1)&=&\\ \psi_\Omega(\Omega^{\Omega+1})\\ \\ (0,0)(1,1)(2,1)(3,1)(2,1)(3,1)&=&\\ \psi_\Omega(\Omega^{\Omega\cdot 2})\\ \\ (0,0)(1,1)(2,1)(3,1)(3,1)&=&\\ \psi_\Omega(\Omega^{\Omega^2})\\ \\ (0,0)(1,1)(2,1)(3,1)(4,1)&=&\\ \psi_\Omega(\Omega^{\Omega^\Omega})\\ \\ (0,0)(1,1)(2,2)&=&\\ \psi_\Omega(\epsilon_{\Omega+1})\\ \\ (0,0)(1,1)(2,2)(2,2)&=&\\ \psi_\Omega(\epsilon_{\Omega+2})\\ \\ (0,0)(1,1)(2,2)(3,2)&=&\\ \psi_\Omega(\zeta_{\Omega+1})\\ \\ (0,0)(1,1)(2,2)(3,3)&=&\\ \psi_\Omega(\psi_{\Omega_2}(\epsilon_{\Omega_2+1}))\\ \\ (0,0)(1,1)(2,2)(3,3)(4,3)&=&\\ \psi_\Omega(\psi_{\Omega_2}(\zeta_{\Omega_2+1}))\\ \\ (0,0,0)(1,1,1)&=&\\ \psi_\Omega(\Omega_\omega)\\ \\ (0,0,0)(1,1,1)(1,1,0)(2,2,1)&=&\\ \psi_\Omega(\Omega_\omega+\psi_{\Omega}(\Omega_\omega))\\ \\ (0,0,0)(1,1,1)(1,1,1)&=&\\ \psi_\Omega(\Omega_\omega\cdot 2)\\ \\ (0,0,0)(1,1,1)(2,0,0)&=&\\ \psi_\Omega(\Omega_\omega\cdot \omega)&=&\\ \psi_\Omega(\Omega\cdot(\Omega_\omega+1))\\ \\ (0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,2,1)(3,0,0)&=&\\ \psi_\Omega(\Omega_\omega\cdot \omega+\psi_{\Omega_2}(\Omega_\omega\cdot \omega))&=&\\ \psi_\Omega(\Omega\cdot(\Omega_\omega+\psi_{\Omega_2}(\Omega_2\cdot(\Omega_\omega+1))))\\ \\ (0,0,0)(1,1,1)(2,0,0)(1,1,1)&=&\\ \psi_\Omega(\Omega_\omega^2)\\ \\ (0,0,0)(1,1,1)(2,1,0)&=&\\ \psi_\Omega(\Omega_\omega^\Omega)&=&\\ \psi_\Omega((\Omega^{\Omega_\omega})^\Omega)&=&\\ \psi_\Omega(\Omega^{\Omega_\omega\cdot\Omega})\\ \\ (0,0,0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,2,0)&=&\\ \psi_\Omega(\Omega^{\Omega_\omega\cdot\psi_{\Omega_2}({\Omega_2}^{\Omega_\omega\cdot{\Omega_2}})})\\ \\ (0,0,0)(1,1,1)(2,1,0)(1,1,1)&=&\\ \psi_\Omega(\Omega_\omega^{\Omega_\omega})\\ \\ (0,0,0)(1,1,1)(2,1,0)(1,1,1)(1,1,1)&=&\\ \psi_\Omega(\Omega_\omega^{\Omega_\omega}+\Omega_\omega)\\ \\ (0,0,0)(1,1,1)(2,1,0)(1,1,1)(2,1,0)&=&\\ \psi_\Omega(\Omega_\omega^{\Omega_\omega}+\Omega_\omega^\Omega)\\ \\ (0,0,0)(1,1,1)(2,1,0)(1,1,1)(2,1,0)(1,1,1)&=&\\ \psi_\Omega(\Omega_\omega^{\Omega_\omega}\cdot 2)\\ \\ (0,0,0)(1,1,1)(2,1,0)(1,1,1)(2,1,0)(1,1,1)&=&\\ \psi_\Omega(\Omega_\omega^{\Omega_\omega}\cdot 3)\\ \\ (0,0,0)(1,1,1)(2,1,0)(2,0,0)&=&\\ \psi_\Omega(\Omega_\omega^{\Omega_\omega}\cdot \omega)\\ \\ (0,0,0)(1,1,1)(2,1,0)(2,1,0)(1,1,1)&=&\\ \psi_\Omega(\Omega_\omega^{\Omega_\omega\cdot 2})\\ \\ (0,0,0)(1,1,1)(2,1,0)(3,0,0)&=&\\ \psi_\Omega(\Omega_\omega^{\Omega_\omega\cdot \omega})\\ \\ (0,0,0)(1,1,1)(2,1,0)(3,0,0)(1,1,1)&=&\\ \psi_\Omega(\Omega_\omega^{\Omega_\omega^2})\\ \\ (0,0,0)(1,1,1)(2,1,0)(3,1,0)(1,1,1)\\ \psi_\Omega(\Omega_\omega^{\Omega_\omega^{\Omega_\omega}}))\\ \\ (0,0,0)(1,1,1)(2,1,0)(3,2,0)&=&\\ \psi_\Omega(\epsilon_{\Omega_{\omega}+1})))&=&\\ \psi_\Omega(\psi_{\Omega_{\omega+1}}(0))\\ \\ (0,0,0)(1,1,1)(2,1,0)(3,2,0)(3,2,0)&=&\\ \psi_\Omega(\epsilon_{\Omega_{\omega}+2})))&=&\\ \psi_\Omega(\psi_{\Omega_{\omega+1}}(1))\\ \\ (0,0,0)(1,1,1)(2,1,0)(3,2,1)&=&\\ \psi_\Omega(\psi_{\Omega_{\omega+1}}(\Omega_{\omega\cdot2}))))\\ \\ (0,0,0)(1,1,1)(2,1,1)&=&\\ \psi_\Omega(\Omega_{\omega^2})))\\ \\ (0,0,0)(1,1,1)(2,1,1)(2,1,1)&=&\\ \psi_\Omega(\Omega_{\omega^3})))\\ \\ (0,0,0)(1,1,1)(2,1,1)(3,0,0)&=&\\ \psi_\Omega(\Omega_{\omega^\omega})))\\ \\ (0,0,0)(1,1,1)(2,1,1)(3,1,0)&=&\\ \psi_\Omega(\Omega_{\Omega})))\\ \\ (0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,1)&=&\\ \psi_\Omega(\Omega_{\Omega_\omega})))\\ \\ (0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,0)\\ (3,2,1)(4,2,1)(5,1,0)(6,2,1)(7,2,1)&=&\\ \psi_\Omega(\Omega_{\psi_{\Omega_{\omega}}(\Omega_{\omega^2})})))\\ \\ (0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)&=&\\ \psi_\Omega(\Omega_{\Omega_{\omega^2}})))\\ \\ (0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)\\ (3,1,0)&=&\\ \psi_\Omega(\Omega_{\Omega_{\Omega}})))\\ \\ (0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)&=&\\ \psi_\Omega(\psi_I(0))\\ \\ (0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,1)\\ (4,2,1)(5,2,0)(3,0,0)&=&\\ \psi_\Omega(\psi_{\Omega_{\psi_I(0)+1}}(\psi_I(1)))\\ \\ (0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,1)&=&\\ \psi_\Omega(\psi_I(\omega))))\\ \\ (0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)\\ (2,0,0)&=&\\ \psi_\Omega(\psi_I(I))))\\ \\ (0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)\\ (6,2,0)(5,0,0)&=&\\ \psi_\Omega(\psi_I(\psi_{\Omega_{I+1}}(\psi_{I_2}(0))))))\\ \\ (0,0,0)(1,1,1)(2,1,1)(3,1,1)&=&\\ \psi_\Omega(I_\omega)\\ \\ \end{array}