BHM分析Part1：0~FSO

本条目展示BHM强度分析的第一部分。使用 $v e b l e n$ 函数。

\begin{aligned} & \varnothing=0\\&(0)=1\\&(0)(0)=2\\&(0)(1)=\omega\\&(0)(1)(0)=\omega+1\\&(0)(1)(0)(0)=\omega+2\\&(0)(1)(0)(0)(1)=\omega\times2\\&(0)(1)(0)(0)(1)(0)=\omega\times2+1\\&(0)(1)(0)(0)(1)(0)(0)(1)=\omega\times3\\&(0)(1)(0)(1)=\omega^2\\&(0)(1)(0)(1)(0)=\omega^2+1\\&(0)(1)(0)(1)(0)(0)(1)=\omega^2+\omega\\&(0)(1)(0)(1)(0)(0)(1)(0)(0)(1)=\omega^2+\omega\times2\\&(0)(1)(0)(1)(0)(0)(1)(0)(1)=\omega^2\times2\\&(0)(1)(0)(1)(0)(0)(1)(0)(1)(0)(0)(1)(0)(1)=\omega^2\times3\\&(0)(1)(0)(1)(0)(1)=\omega^3\\&(0)(1)(0)(1)(0)(1)(0)(0)(1)(0)(1)(0)(1)=\omega^3\times2\\&(0)(1)(0)(1)(0)(1)(0)(1)=\omega^4\\&(0)(1)(1)=\omega^\omega\\&(0)(1)(1)(0)(0)(1)=\omega^\omega+\omega\\&(0)(1)(1)(0)(0)(1)(0)(1)=\omega^\omega+\omega^2\\&(0)(1)(1)(0)(0)(1)(1)=\omega^\omega\times2\\&(0)(1)(1)(0)(1)=\omega^{\omega+1}\\&(0)(1)(1)(0)(1)(0)(0)(1)(1)=\omega^{\omega+1}+\omega^\omega\\&(0)(1)(1)(0)(1)(0)(0)(1)(1)(0)(1)=\omega^{\omega+1}\times2\\&(0)(1)(1)(0)(1)(0)(1)=\omega^{\omega+2}\\&(0)(1)(1)(0)(1)(0)(1)(1)=\omega^{\omega\times2}\\&(0)(1)(1)(0)(1)(0)(1)(1)(0)(1)=\omega^{\omega\times2+1}\\&(0)(1)(1)(0)(1)(0)(1)(1)(0)(1)(0)(1)(1)=\omega^{\omega\times3}\\&(0)(1)(1)(0)(1)(1)=\omega^{\omega^2}\\&(0)(1)(1)(0)(1)(1)(0)(1)=\omega^{\omega^2+1}\\&(0)(1)(1)(0)(1)(1)(0)(1)(0)(1)(1)=\omega^{\omega^2+\omega}\\&(0)(1)(1)(0)(1)(1)(0)(1)(0)(1)(1)(0)(1)(1)=\omega^{\omega^2\times2}\\&(0)(1)(1)(0)(1)(1)(0)(1)(1)=\omega^{\omega^3}\\&(0)(1)(1)(1)=\omega^{\omega^\omega}\\&(0)(1)(1)(1)(0)(0)(1)(1)(1)=\omega^{\omega^\omega}\times2\\&(0)(1)(1)(1)(0)(1)=\omega^{\omega^\omega+1}\\&(0)(1)(1)(1)(0)(1)(0)(1)(1)(1)=\omega^{\omega^\omega\times2}\\&(0)(1)(1)(1)(0)(1)(1)=\omega^{\omega^{\omega+1}}\\&(0)(1)(1)(1)(0)(1)(1)(0)(1)(1)=\omega^{\omega^{\omega+2}}\\&(0)(1)(1)(1)(0)(1)(1)(0)(1)(1)(1)=\omega^{\omega^{\omega\times2}}\\&(0)(1)(1)(1)(0)(1)(1)(1)=\omega^{\omega^{\omega^2}}\\&(0)(1)(1)(1)(0)(1)(1)(1)(0)(1)(1)(1)=\omega^{\omega^{\omega^3}}\\&(0)(1)(1)(1)(1)=\omega^{\omega^{\omega^\omega}}\\&(0)(1)(1)(1)(1)(1)=\omega^{\omega^{\omega^{\omega^\omega}}}\\&(0)(1)(2)=\varepsilon_0\\&(0)(1)(2)(0)(0)(1)(2)=\varepsilon_0\times2\\&(0)(1)(2)(0)(1)=\omega^{\varepsilon_0+1}\\&(0)(1)(2)(0)(1)(0)(1)=\omega^{\varepsilon_0+2}\\&(0)(1)(2)(0)(1)(0)(1)(1)=\omega^{\varepsilon_0+\omega}\\&(0)(1)(2)(0)(1)(0)(1)(1)(0)(1)(0)(1)(1)=\omega^{\varepsilon_0+\omega\times2}\\&(0)(1)(2)(0)(1)(0)(1)(1)(0)(1)(1)=\omega^{\varepsilon_0+\omega^2}\\&(0)(1)(2)(0)(1)(0)(1)(1)(1)=\omega^{\varepsilon_0+\omega^\omega}\\&(0)(1)(2)(0)(1)(0)(1)(1)(1)(1)=\omega^{\varepsilon_0+\omega^{\omega^\omega}}\\&(0)(1)(2)(0)(1)(0)(1)(2)=\omega^{\varepsilon_0\times2}\\&(0)(1)(2)(0)(1)(0)(1)(2)(0)(1)=\omega^{\varepsilon_0\times2+1}\\&(0)(1)(2)(0)(1)(0)(1)(2)(0)(1)(0)(1)(2)=\omega^{\varepsilon_0\times3}\\&(0)(1)(2)(0)(1)(1)=\omega^{\omega^{\varepsilon_0+1}}\\&(0)(1)(2)(0)(1)(1)(0)(1)=\omega^{\omega^{\varepsilon_0+1}+1}\\&(0)(1)(2)(0)(1)(1)(0)(1)(0)(1)(2)(0)(1)(1)=\omega^{\omega^{\varepsilon_0+1}\times2}\\&(0)(1)(2)(0)(1)(1)(0)(1)(1)=\omega^{\omega^{\varepsilon_0+2}}\\&(0)(1)(2)(0)(1)(1)(0)(1)(1)(1)=\omega^{\omega^{\varepsilon_0+\omega}}\\&(0)(1)(2)(0)(1)(1)(0)(1)(1)(1)(1)=\omega^{\omega^{\varepsilon_0+\omega^\omega}}\\&(0)(1)(2)(0)(1)(1)(0)(1)(2)=\omega^{\omega^{\varepsilon_0\times2}}\\&(0)(1)(2)(0)(1)(1)(1)=\omega^{\omega^{\omega^{\varepsilon_0+1}}}\\&(0)(1)(2)(0)(1)(1)(1)(1)=\omega^{\omega^{\omega^{\omega^{\varepsilon_0+1}}}}\\&(0)(1)(2)(0)(1)(2)=\varepsilon_1\\&(0)(1)(2)(0)(1)(2)(0)(1)=\omega^{\varepsilon_1+1}\\&(0)(1)(2)(0)(1)(2)(0)(1)(0)(1)(2)=\omega^{\varepsilon_1+\varepsilon_0}\\&(0)(1)(2)(0)(1)(2)(0)(1)(0)(1)(2)(0)(1)(2)=\omega^{\varepsilon_1\times2}\\&(0)(1)(2)(0)(1)(2)(0)(1)(1)=\omega^{\omega^{\varepsilon_1+1}}\\&(0)(1)(2)(0)(1)(2)(0)(1)(1)(1)=\omega^{\omega^{\omega^{\varepsilon_1+1}}}\\&(0)(1)(2)(0)(1)(2)(0)(1)(2)=\varepsilon_2\\&(0)(1)(2)(1)=\varepsilon_\omega\\&(0)(1)(2)(1)(0)(1)=\omega^{\varepsilon_\omega+1}\\&(0)(1)(2)(1)(0)(1)(0)(1)(2)(0)(1)(2)=\omega^{\varepsilon_\omega+\varepsilon_1}\\&(0)(1)(2)(1)(0)(1)(0)(1)(2)(1)=\omega^{\varepsilon_\omega\times2}\\&(0)(1)(2)(1)(0)(1)(1)=\omega^{\omega^{\varepsilon_\omega+1}}\\&(0)(1)(2)(1)(0)(1)(2)=\varepsilon_{\omega+1}\\&(0)(1)(2)(1)(0)(1)(2)(0)(1)(2)=\varepsilon_{\omega+2}\\&(0)(1)(2)(1)(0)(1)(2)(0)(1)(2)(1)=\varepsilon_{\omega\times2}\\&(0)(1)(2)(1)(0)(1)(2)(1)=\varepsilon_{\omega^2}\\&(0)(1)(2)(1)(0)(1)(2)(1)(0)(1)(2)(1)=\varepsilon_{\omega^3}\\&(0)(1)(2)(1)(1)=\varepsilon_{\omega^\omega}\\&(0)(1)(2)(1)(1)(0)(1)(2)=\varepsilon_{\omega^\omega+1}\\&(0)(1)(2)(1)(1)(0)(1)(2)(0)(1)(2)(1)(1)=\varepsilon_{\omega^\omega\times2}\\&(0)(1)(2)(1)(1)(0)(1)(2)(1)=\varepsilon_{\omega^{\omega+1}}\\&(0)(1)(2)(1)(1)(0)(1)(2)(1)(0)(1)(2)(1)(1)=\varepsilon_{\omega^{\omega\times2}}\\&(0)(1)(2)(1)(1)(0)(1)(2)(1)(1)=\varepsilon_{\omega^{\omega^2}}\\&(0)(1)(2)(1)(1)(1)=\varepsilon_{\omega^{\omega^\omega}}\\&(0)(1)(2)(1)(1)(2)=\varepsilon_{\varepsilon_0}\\&(0)(1)(2)(1)(1)(2)(0)(1)(2)=\varepsilon_{\varepsilon_0+1}\\&(0)(1)(2)(1)(1)(2)(0)(1)(2)(0)(1)(2)(1)(1)(2)=\varepsilon_{\varepsilon_0\times2}\\&(0)(1)(2)(1)(1)(2)(0)(1)(2)(1)=\varepsilon_{\omega^{\varepsilon_0+1}}\\&(0)(1)(2)(1)(1)(2)(0)(1)(2)(1)(1)=\varepsilon_{\omega^{\omega^{\varepsilon_0+1}}}\\&(0)(1)(2)(1)(1)(2)(0)(1)(2)(1)(1)(2)=\varepsilon_{\varepsilon_1}\\&(0)(1)(2)(1)(1)(2)(0)(1)(2)(1)(1)(2)(0)(1)(2)(1)(1)(2)=\varepsilon_{\varepsilon_2}\\&(0)(1)(2)(1)(1)(2)(1)=\varepsilon_{\varepsilon_\omega}\\&(0)(1)(2)(1)(1)(2)(1)(0)(1)(2)(1)(1)(2)=\varepsilon_{\varepsilon_{\omega+1}}\\&(0)(1)(2)(1)(1)(2)(1)(0)(1)(2)(1)(1)(2)(0)(1)(2)(1)(1)(2)(1)=\varepsilon_{\varepsilon_{\omega\times2}}\\&(0)(1)(2)(1)(1)(2)(1)(0)(1)(2)(1)(1)(2)(1)=\varepsilon_{\varepsilon_{\omega^2}}\\&(0)(1)(2)(1)(1)(2)(1)(1)=\varepsilon_{\varepsilon_{\omega^\omega}}\\&(0)(1)(2)(1)(1)(2)(1)(1)(1)=\varepsilon_{\varepsilon_{\omega^{\omega^\omega}}}\\&(0)(1)(2)(1)(1)(2)(1)(1)(2)=\varepsilon_{\varepsilon_{\varepsilon_0}}\\&(0)(1)(2)(1)(1)(2)(1)(1)(2)(0)(1)(2)(1)(1)(2)(1)(1)(2)=\varepsilon_{\varepsilon_{\varepsilon_1}}\\&(0)(1)(2)(1)(1)(2)(1)(1)(2)(1)=\varepsilon_{\varepsilon_{\varepsilon_\omega}}\\&(0)(1)(2)(1)(2)=\zeta_0\\&(0)(1)(2)(1)(2)(0)(1)(2)=\varepsilon_{\zeta_0+1}\\&(0)(1)(2)(1)(2)(0)(1)(2)(0)(1)(2)(1)(2)=\varepsilon_{\zeta_0\times2}\\&(0)(1)(2)(1)(2)(0)(1)(2)(1)=\varepsilon_{\omega^{\zeta_0+1}}\\&(0)(1)(2)(1)(2)(0)(1)(2)(1)(1)(2)=\varepsilon_{\varepsilon_{\zeta_0+1}}\\&(0)(1)(2)(1)(2)(0)(1)(2)(1)(1)(2)(0)(1)(2)(1)(2)=\varepsilon_{\varepsilon_{\zeta_0\times2}}\\&(0)(1)(2)(1)(2)(0)(1)(2)(1)(1)(2)(1)=\varepsilon_{\varepsilon_{\omega^{\zeta_0+1}}}\\&(0)(1)(2)(1)(2)(0)(1)(2)(1)(1)(2)(1)(1)(2)=\varepsilon_{\varepsilon_{\varepsilon_{\zeta_0+1}}}\\&(0)(1)(2)(1)(2)(0)(1)(2)(1)(2)=\zeta_1\\&(0)(1)(2)(1)(2)(0)(1)(2)(1)(2)(0)(1)(2)(1)(2)=\zeta_2\\&(0)(1)(2)(1)(2)(1)=\zeta_\omega\\&(0)(1)(2)(1)(2)(1)(0)(1)(2)(1)(2)=\zeta_{\omega+1}\\&(0)(1)(2)(1)(2)(1)(0)(1)(2)(1)(2)(0)(1)(2)(1)(2)(1)=\zeta_{\omega\times2}\\&(0)(1)(2)(1)(2)(1)(0)(1)(2)(1)(2)(1)=\zeta_{\omega^2}\\&(0)(1)(2)(1)(2)(1)(1)=\zeta_{\omega^\omega}\\&(0)(1)(2)(1)(2)(1)(1)(2)=\zeta_{\varepsilon_0}\\&(0)(1)(2)(1)(2)(1)(1)(2)(0)(1)(2)(1)(2)=\zeta_{\varepsilon_0+1}\\&(0)(1)(2)(1)(2)(1)(1)(2)(0)(1)(2)(1)(2)(0)(1)(2)(1)(2)(1)(1)(2)=\zeta_{\varepsilon_0\times2}\\&(0)(1)(2)(1)(2)(1)(1)(2)(0)(1)(2)(1)(2)(1)=\zeta_{\omega^{\varepsilon_0+1}}\\&(0)(1)(2)(1)(2)(1)(1)(2)(0)(1)(2)(1)(2)(1)(1)(2)=\zeta_{\varepsilon_1}\\&(0)(1)(2)(1)(2)(1)(1)(2)(1)=\zeta_{\varepsilon_\omega}\\&(0)(1)(2)(1)(2)(1)(1)(2)(1)(1)(2)=\zeta_{\varepsilon_{\varepsilon_0}}\\&(0)(1)(2)(1)(2)(1)(1)(2)(1)(1)(2)(1)(1)(2)=\zeta_{\varepsilon_{\varepsilon_{\varepsilon_0}}}\\&(0)(1)(2)(1)(2)(1)(1)(2)(1)(2)=\zeta_{\zeta_0}\\&(0)(1)(2)(1)(2)(1)(1)(2)(1)(2)(0)(1)(2)(1)(2)=\zeta_{\zeta_0+1}\\&(0)(1)(2)(1)(2)(1)(1)(2)(1)(2)(0)(1)(2)(1)(2)(1)(1)(2)=\zeta_{\varepsilon_{\zeta_0+1}}\\&(0)(1)(2)(1)(2)(1)(1)(2)(1)(2)(0)(1)(2)(1)(2)(1)(1)(2)(1)(2)=\zeta_{\zeta_1}\\&(0)(1)(2)(1)(2)(1)(1)(2)(1)(2)(1)=\zeta_{\zeta_\omega}\\&(0)(1)(2)(1)(2)(1)(1)(2)(1)(2)(1)(1)(2)=\zeta_{\zeta_{\varepsilon_0}}\\&(0)(1)(2)(1)(2)(1)(1)(2)(1)(2)(1)(1)(2)(1)(2)=\zeta_{\zeta_{\zeta_0}}\\&(0)(1)(2)(1)(2)(1)(2)=\eta_0\\&(0)(1)(2)(1)(2)(1)(2)(0)(1)(2)=\varepsilon_{\eta_0+1}\\&(0)(1)(2)(1)(2)(1)(2)(0)(1)(2)(1)(2)=\zeta_{\eta_0+1}\\&(0)(1)(2)(1)(2)(1)(2)(0)(1)(2)(1)(2)(1)(2)=\eta_1\\&(0)(1)(2)(1)(2)(1)(2)(1)=\eta_\omega\\&(0)(1)(2)(1)(2)(1)(2)(1)(1)(2)=\eta_{\varepsilon_0}\\&(0)(1)(2)(1)(2)(1)(2)(1)(1)(2)(1)(2)=\eta_{\zeta_0}\\&(0)(1)(2)(1)(2)(1)(2)(1)(1)(2)(1)(2)(1)(2)=\eta_{\eta_0}\\&(0)(1)(2)(1)(2)(1)(2)(1)(2)=\varphi(4,0)\\&(0)(1)(2)(1)(2)(1)(2)(1)(2)(1)(2)=\varphi(5,0)\\&(0)(1)(2)(2)=\varphi(\omega,0)\\&(0)(1)(2)(2)(0)(1)(2)=\varphi(1,\varphi(\omega,0)+1)\\&(0)(1)(2)(2)(0)(1)(2)(1)(2)=\varphi(2,\varphi(\omega,0)+1)\\&(0)(1)(2)(2)(0)(1)(2)(1)(2)(1)(2)=\varphi(3,\varphi(\omega,0)+1)\\&(0)(1)(2)(2)(0)(1)(2)(2)=\varphi(\omega,1)\\&(0)(1)(2)(2)(0)(1)(2)(2)(0)(1)(2)(2)=\varphi(\omega,2)\\&(0)(1)(2)(2)(1)=\varphi(\omega,\omega)\\&(0)(1)(2)(2)(1)(1)(2)=\varphi(\omega,\varphi(1,0))\\&(0)(1)(2)(2)(1)(1)(2)(1)(2)=\varphi(\omega,\varphi(2,0))\\&(0)(1)(2)(2)(1)(1)(2)(2)=\varphi(\omega,\varphi(\omega,0))\\&(0)(1)(2)(2)(1)(1)(2)(2)(1)(1)(2)(2)=\varphi(\omega,\varphi(\omega,\varphi(\omega,0)))\\&(0)(1)(2)(2)(1)(2)=\varphi(\omega+1,0)\\&(0)(1)(2)(2)(1)(2)(1)(2)=\varphi(\omega+2,0)\\&(0)(1)(2)(2)(1)(2)(1)(2)(2)=\varphi(\omega\times2,0)\\&(0)(1)(2)(2)(1)(2)(1)(2)(2)(1)(2)(1)(2)(2)=\varphi(\omega\times3,0)\\&(0)(1)(2)(2)(1)(2)(2)=\varphi(\omega^2,0)\\&(0)(1)(2)(2)(1)(2)(2)(1)(2)=\varphi(\omega^2+1,0)\\&(0)(1)(2)(2)(1)(2)(2)(1)(2)(1)(2)(2)(1)(2)(2)=\varphi(\omega^2\times2,0)\\&(0)(1)(2)(2)(1)(2)(2)(1)(2)(2)=\varphi(\omega^3,0)\\&(0)(1)(2)(2)(2)=\varphi(\omega^\omega,0)\\&(0)(1)(2)(2)(2)(1)(2)=\varphi(\omega^\omega+1,0)\\&(0)(1)(2)(2)(2)(1)(2)(2)=\varphi(\omega^{\omega+1},0)\\&(0)(1)(2)(2)(2)(1)(2)(2)(2)=\varphi(\omega^{\omega^2},0)\\&(0)(1)(2)(2)(2)(2)=\varphi(\omega^{\omega^\omega},0)\\&(0)(1)(2)(3)=\varphi(\varphi(1,0),0)\\&(0)(1)(2)(3)(1)(2)=\varphi(\varphi(1,0)+1,0)\\&(0)(1)(2)(3)(1)(2)(1)(2)(3)=\varphi(\varphi(1,0)\times2,0)\\&(0)(1)(2)(3)(1)(2)(2)=\varphi(\omega^{\varphi(1,0)+1},0)\\&(0)(1)(2)(3)(1)(2)(2)(2)=\varphi(\omega^{\omega^{\varphi(1,0)+1}},0)\\&(0)(1)(2)(3)(1)(2)(3)=\varphi(\varphi(1,1),0)\\&(0)(1)(2)(3)(2)=\varphi(\varphi(1,\omega),0)\\&(0)(1)(2)(3)(2)(2)=\varphi(\varphi(1,\omega^\omega),0)\\&(0)(1)(2)(3)(2)(2)(3)=\varphi(\varphi(1,\varphi(1,0)),0)\\&(0)(1)(2)(3)(2)(2)(3)(2)(2)(3)=\varphi(\varphi(1,\varphi(1,\varphi(1,0))),0)\\&(0)(1)(2)(3)(2)(3)=\varphi(\varphi(2,0),0)\\&(0)(1)(2)(3)(2)(3)(2)(3)=\varphi(\varphi(3,0),0)\\&(0)(1)(2)(3)(3)=\varphi(\varphi(\omega,0),0)\\&(0)(1)(2)(3)(3)(2)(3)=\varphi(\varphi(\omega+1,0),0)\\&(0)(1)(2)(3)(3)(2)(3)(3)=\varphi(\varphi(\omega^2,0),0)\\&(0)(1)(2)(3)(3)(3)=\varphi(\varphi(\omega^\omega,0),0)\\&(0)(1)(2)(3)(4)=\varphi(\varphi(\varphi(1,0),0),0)\\&(0)(1)(2)(3)(4)(2)(3)(4)=\varphi(\varphi(\varphi(1,1),0),0)\\&(0)(1)(2)(3)(4)(3)(4)=\varphi(\varphi(\varphi(2,0),0),0)\\&(0)(1)(2)(3)(4)(4)=\varphi(\varphi(\varphi(\omega,0),0),0)\\&(0)(1)(2)(3)(4)(5)=\varphi(\varphi(\varphi(\varphi(1,0),0),0),0)\\&(0)(1)(2)(3)(4)(5)(6)=\varphi(\varphi(\varphi(\varphi(\varphi(1,0),0),0),0),0)\\&(0,0)(1,1)=\varphi(1,0,0) \end{aligned}