FANDOM


フェファーマン・シュッテの順序数から先、順序数崩壊関数をつかいます。

分析

\begin{array}{ll} (0)&=&\\ 1&=&\\ \phi_0(0)\\ \\ (0)(0)&=&\\ 2&=&\\ \phi_0(0)+\phi_0(0)\\ \\ (0)(0)(0)&=&\\ 3&=&\\ \phi_0(0)+\phi_0(0)+\phi_0(0)\\ \\ (0)(1)&=&\\ \phi_0(1)\\ \\ (0)(1)(0)(1)&=&\\ \phi_0(1)+\phi_0(1)\\ \\ (0)(1)(1)&=&\\ \phi_0(2)\\ \\ (0)(1)(1)(1)&=&\\ \phi_0(3)\\ \\ (0)(1)(2)&=&\\ \phi_0(\phi_0(1))&=&\\ \phi^2_0(1)&=&\\ \phi^3_0(0)\\ \\ (0)(1)(2)(1)&=&\\ \phi_0(\phi_0(1)+1)\\ \\ (0)(1)(2)(3)&=&\\ \phi_0^4(0)\\ \\ (0,0)(1,1)&=&\\ \phi_1(0)\\ \\ (0,0)(1,1)(1,0)&=&\\ \phi_0(\phi_1(0)+1)\\ \\ (0,0)(1,1)(1,0)(2,1)&=&\\ \phi_0(\phi_1(0)+\phi_1(0))\\ \\ (0,0)(1,1)(1,0)(2,1)(2,0)&=&\\ \phi_0(\phi_0(\phi_1(0)+1))&=&\\ \phi_0^2(\phi_1(0)+1)\\ \\ (0,0)(1,1)(1,1)&=&\\ \phi_1(1)&>&\\ \phi_0^n(\phi_1(0)+1)\\ \\ (0,0)(1,1)(1,1)(1,1)&=&\\ \phi_1(2)&>&\\ \phi_0^n(\phi_1(1)+1)\\ \\ (0,0)(1,1)(2,0)&=&\\ \phi_1(\phi_0(1))\\ \\ (0,0)(1,1)(2,0)(3,1)&=&\\ \phi_1(\phi_1(0))&=&\\ \phi_1^2(0)\\ \\ (0,0)(1,1)(2,1)&=&\\ \phi_2(0)\\ \\ (0,0)(1,1)(2,1)(1,0)&=&\\ \phi_0(\phi_2(0)+1)\\ \\ (0,0)(1,1)(2,1)(1,1)&=&\\ \phi_1(\phi_2(0)+1)\\ \\ (0,0)(1,1)(2,1)(1,1)(2,0)&=&\\ \phi_1(\phi_2(0)+\phi_0(1))\\ \\ (0,0)(1,1)(2,1)(1,1)(2,0)(3,1)&=&\\ \phi_1(\phi_2(0)+\phi_1(0))\\ \\ (0,0)(1,1)(2,1)(1,1)(2,0)(3,1)(4,1)&=&\\ \phi_1(\phi_2(0)+\phi_2(0))\\ \\ (0,0)(1,1)(2,1)(1,1)(2,0)(3,1)(4,1)(3,0)&=&\\ \phi_1(\phi_0(\phi_2(0)+1))\\ \\ (0,0)(1,1)(2,1)(1,1)(2,0)(3,1)(4,1)(3,1)&=&\\ \phi_1^2(\phi_2(0)+1)\\ \\ (0,0)(1,1)(2,1)(1,1)(2,1)&=&\\ \phi_2(1)\\ \\ (0,0)(1,1)(2,1)(2,0)&=&\\ \phi_2(\phi_0(1))\\ \\ (0,0)(1,1)(2,1)(2,0)(3,1)&=&\\ \phi_2(\phi_1(0))\\ \\ (0,0)(1,1)(2,1)(2,0)(3,1)(4,1)&=&\\ \phi_2^2(0)\\ \\ (0,0)(1,1)(2,1)(2,1)&=&\\ \phi_3(0)\\ \\ (0,0)(1,1)(2,1)(2,1)(2,1)&=&\\ \phi_4(0)\\ \\ (0,0)(1,1)(2,1)(3,0)&=&\\ \phi_{\phi_0(1)}(0)&>&\\ \phi_n(0)\\ \\ (0,0)(1,1)(2,1)(3,0)(2,1)&=&\\ \phi_{\phi_0(1)+1}(0)\\ \\ (0,0)(1,1)(2,1)(3,0)(3,0)&=&\\ \phi_{\phi_0(2)}(0)\\ \\ (0,0)(1,1)(2,1)(3,0)(4,1)&=&\\ \phi_{\phi_1(0)}(0)&=&\\ \phi_{\phi_{\phi_0(0)}(0)}\\ \\ (0,0)(1,1)(2,1)(3,1)&=&\\ \Gamma_0&=&\\ \\ \psi(0)\\ (0,0)(1,1)(2,1)(3,1)(1,1)&=&\\ \phi_1(\psi_\Omega(0)+1)\\ \\ (0,0)(1,1)(2,1)(3,1)(1,1)(2,1)(3,0)&=&\\ \phi_\omega(\psi_\Omega(0)+1)\\ \\ (0,0)(1,1)(2,1)(3,1)(1,1)(2,1)(3,1)&=&\\ \psi_\Omega(1)\\ \\ (0,0)(1,1)(2,1)(3,1)(2,0)&=&\\ \psi_\Omega(\omega)\\ \\ (0,0)(1,1)(2,1)(3,1)(2,0)(1,1)(2,1)(3,1)&=&\\ \psi_\Omega(\omega+1)\\ \\ (0,0)(1,1)(2,1)(3,1)(2,0)(3,1)(4,1)(5,1)&=&\\ \psi_\Omega^2(0)\\ \\ (0,0)(1,1)(2,1)(3,1)(2,1)&=&\\ \psi_\Omega(\Omega)&>&\\ \psi_\Omega^n(0)\\ \\ (0,0)(1,1)(2,1)(3,1)(2,1)(1,1)(2,1)(3,1)(2,1)&=&\\ \psi_\Omega(\Omega+\Omega)&>&\\ (\lambda x.\psi_\Omega(\Omega+x))^n0\\\ \\ \end{array}