查看“︁BHM分析”︁的源代码

本条目展示 [[BHM]] 的强度的列表分析。

=== Part 1 ===
{| class="wikitable"
!BHM
!Veblen 函数
!
!
|-
|<math>(0)</math>
|<math>1</math>
|-
|<math>(0)(0)</math>
|<math>2</math>
|-
|<math>(0)(0)(0)</math>
|<math>3</math>
|-
|<math>(0)(1)</math>
|<math>\omega</math>
|-
|<math>(0)(1)(0)</math>
|<math>\omega +1</math>
|-
|<math>(0)(1)(0)(0)</math>
|<math>\omega +2</math>
|-
|<math>(0)(1)(0)(0)(1)</math>
|<math>\omega \times 2</math>
|-
|<math>(0)(1)(0)(0)(1)(0)</math>
|<math>\omega \times 2 +1</math>
|-
|<math>(0)(1)(0)(0)(1)(0)(0)(1)</math>
|<math>\omega \times 3</math>
|-
|<math>(0)(1)(0)(1)</math>
|<math>\omega ^2</math>
|-
|<math>(0)(1)(0)(1)(0)</math>
|<math>\omega ^2+1</math>
|-
|<math>(0)(1)(0)(1)(0)(0)(1)</math>
|<math>\omega ^2+\omega</math>
|-
|<math>(0)(1)(0)(1)(0)(0)(1)(0)(0)(1)</math>
|<math>\omega ^2+\omega\times 2</math>
|-
|<math>(0)(1)(0)(1)(0)(0)(1)(0)(1)</math>
|<math>\omega ^2\times 2</math>
|-
|<math>(0)(1)(0)(1)(0)(0)(1)(0)(1)(0)(0)(1)</math>
|<math>\omega ^2\times 2 + \omega</math>
|-
|<math>(0)(1)(0)(1)(0)(1)</math>
|<math>\omega ^3</math>
|-
|<math>(0)(1)(1)</math>
|<math>\omega ^\omega</math>
|-
|<math>(0)(1)(1)(0)</math>
|<math>\omega ^\omega+1</math>
|-
|<math>(0)(1)(1)(0)(0)(1)</math>
|<math>\omega ^\omega+\omega</math>
|-
|<math>(0)(1)(1)(0)(0)(1)(0)(1)</math>
|<math>\omega ^\omega+\omega\times 2</math>
|-
|<math>(0)(1)(1)(0)(0)(1)(1)</math>
|<math>\omega ^\omega \times 2</math>
|-
|<math>(0)(1)(1)(0)(1)</math>
|<math>\omega ^{\omega +1}</math>
|-
|<math>(0)(1)(1)(0)(1)(0)(0)(1)</math>
|<math>\omega ^{\omega +1}+\omega</math>
|-
|<math>(0)(1)(1)(0)(1)(0)(0)(1)(1)</math>
|<math>\omega ^{\omega +1}+\omega^{\omega}</math>
|-
|<math>(0)(1)(1)(0)(1)(0)(0)(1)(1)(0)(1)</math>
|<math>\omega ^{\omega +1}\times 2</math>
|-
|<math>(0)(1)(1)(0)(1)(0)(1)</math>
|<math>\omega ^{\omega +2}</math>
|-
|<math>(0)(1)(1)(0)(1)(0)(1)(1)</math>
|<math>\omega ^{\omega \times 2}</math>
|-
|<math>(0)(1)(1)(0)(1)(0)(1)(1)(0)(1)</math>
|<math>\omega ^{\omega \times 2+1}</math>
|-
|<math>(0)(1)(1)(0)(1)(0)(1)(1)(0)(1)(0)(1)(1)</math>
|<math>\omega ^{\omega \times 3}</math>
|-
|<math>(0)(1)(1)(0)(1)(1)</math>
|<math>\omega ^{\omega ^2}</math>
|-
|<math>(0)(1)(1)(0)(1)(1)(0)(1)(0)(1)(1)</math>
|<math>\omega ^{\omega ^2+\omega}</math>
|-
|<math>(0)(1)(1)(0)(1)(1)(0)(1)(0)(1)(1)</math>
|<math>\omega ^{\omega ^2\times 2}</math>
|-
|<math>(0)(1)(1)(0)(1)(1)(0)(1)(1)</math>
|<math>\omega ^{\omega ^3}</math>
|-
|<math>(0)(1)(1)(1)</math>
|<math>\omega ^{\omega ^\omega}</math>
|-
|<math>(0)(1)(1)(1)(0)(1)(1)</math>
|<math>\omega ^{\omega ^{\omega+1}}</math>
|-
|<math>(0)(1)(1)(1)(0)(1)(1)(0)(1)(1)(1)</math>
|<math>\omega ^{\omega ^{\omega\times 2}}</math>
|-
|<math>(0)(1)(1)(1)(0)(1)(1)(1)</math>
|<math>\omega ^{\omega ^{\omega^2}}</math>
|-
|<math>(0)(1)(1)(1)(1)</math>
|<math>\omega ^{\omega ^{\omega^\omega}}</math>
|-
|<math>(0)(1)(2)</math>
|<math>\varepsilon_0</math>
|}

=== Part 2 ===
{| class="wikitable"
!BHM
!Veblen 函数
!
!
|-
|<math>(0)(1)(2)(0)(0)(1)</math>
|<math>\varepsilon_0 + \omega</math>
|-
|<math>(0)(1)(2)(0)(0)(1)(1)</math>
|<math>\varepsilon_0 +\omega^2</math>
|-
|<math>(0)(1)(2)(0)(0)(1)(2)</math>
|<math>\varepsilon_0 \times 2</math>
|-
|<math>(0)(1)(2)(0)(1)</math>
|<math>\varepsilon_0 \times \omega</math>
|-
|<math>(0)(1)(2)(0)(1)(0)(1)(1)</math>
|<math>\varepsilon_0 \times \omega^\omega</math>
|-
|<math>(0)(1)(2)(0)(1)(0)(1)(2)</math>
|<math>\varepsilon_0 ^2</math>
|-
|<math>(0)(1)(2)(0)(1)(0)(1)(2)(0)(1)(0)(1)(2)</math>
|<math>\varepsilon_0 ^3</math>
|-
|<math>(0)(1)(2)(0)(1)(1)</math>
|<math>\varepsilon_0 ^\omega</math>
|-
|<math>(0)(1)(2)(0)(1)(1)(0)(1)(0)(1)(2)</math>
|<math>\varepsilon_0 ^{\omega+1}</math>
|-
|<math>(0)(1)(2)(0)(1)(1)(0)(1)(0)(1)(2)(0)(1)(1)</math>
|<math>\varepsilon_0 ^{\omega\times 2}</math>
|-
|<math>(0)(1)(2)(0)(1)(1)(0)(1)(1)</math>
|<math>\varepsilon_0 ^{\omega^2}</math>
|-
|<math>(0)(1)(2)(0)(1)(1)(0)(1)(1)(1)</math>
|<math>\varepsilon_0 ^{\omega^\omega}</math>
|-
|<math>(0)(1)(2)(0)(1)(1)(0)(1)(2)</math>
|<math>\varepsilon_0 ^{\varepsilon_0}</math>
|-
|<math>(0)(1)(2)(0)(1)(1)(1)</math>
|<math>\varepsilon_0 ^{\varepsilon_0\times \omega}</math>
|-
|<math>(0)(1)(2)(0)(1)(1)(1)(0)(1)(2)</math>
|<math>\varepsilon_0 ^{\varepsilon_0^2}</math>
|-
|<math>(0)(1)(2)(0)(1)(1)(1)(1)</math>
|<math>\varepsilon_0 ^{\varepsilon_0^\omega}</math>
|-
|<math>(0)(1)(2)(0)(1)(1)(1)(1)(0)(1)(2)</math>
|<math>\varepsilon_0 ^{\varepsilon_0^{\varepsilon_0}}</math>
|-
|<math>(0)(1)(2)(0)(1)(2)</math>
|<math>\varepsilon_1 </math>
|-
|<math>(0)(1)(2)(0)(1)(2)(0)(1)</math>
|<math>\varepsilon_1 \times \omega</math>
|-
|<math>(0)(1)(2)(0)(1)(2)(0)(1)(0)(1)(2)</math>
|<math>\varepsilon_1 \times \varepsilon_0</math>
|-
|<math>(0)(1)(2)(0)(1)(2)(0)(1)(0)(1)(2)(0)(1)(1)(0)(1)(2)</math>
|<math>\varepsilon_1 \times \varepsilon_0^{\varepsilon_0}</math>
|-
|<math>(0)(1)(2)(0)(1)(2)(0)(1)(0)(1)(2)(0)(1)(2)</math>
|<math>\varepsilon_1 ^2</math>
|-
|<math>(0)(1)(2)(0)(1)(2)(0)(1)(1)</math>
|<math>\varepsilon_1 ^\omega</math>
|-
|<math>(0)(1)(2)(0)(1)(2)(0)(1)(1)(0)(1)(2)</math>
|<math>\varepsilon_1 ^{\varepsilon_0}</math>
|-
|<math>(0)(1)(2)(0)(1)(2)(0)(1)(1)(0)(1)(2)(0)(1)(2)</math>
|<math>\varepsilon_1 ^{\varepsilon_1}</math>
|-
|<math>(0)(1)(2)(0)(1)(2)(0)(1)(2)</math>
|<math>\varepsilon_2</math>
|-
|<math>(0)(1)(2)(1)</math>
|<math>\varepsilon_\omega </math>
|-
|<math>(0)(1)(2)(1)(0)(1)(2)</math>
|<math>\varepsilon_{\omega +1} </math>
|-
|<math>(0)(1)(2)(1)(0)(1)(2)(0)(1)(2)(1)</math>
|<math>\varepsilon_{\omega \times 2} </math>
|-
|<math>(0)(1)(2)(1)(0)(1)(2)(1)</math>
|<math>\varepsilon_{\omega ^2} </math>
|-
|<math>(0)(1)(2)(1)(1)</math>
|<math>\varepsilon_{\omega ^\omega} </math>
|-
|<math>(0)(1)(2)(1)(1)(2)</math>
|<math>\varepsilon_{\varepsilon_0} </math>
|-
|<math>(0)(1)(2)(1)(1)(2)(0)(1)(2)(1)</math>
|<math>\varepsilon_{\varepsilon_0 \times \omega} </math>
|-
|<math>(0)(1)(2)(1)(1)(2)(0)(1)(2)(1)(0)(1)(2)(1)(1)(2)</math>
|<math>\varepsilon_{\varepsilon_0 ^2} </math>
|-
|<math>(0)(1)(2)(1)(1)(2)(0)(1)(2)(1)(1)</math>
|<math>\varepsilon_{\varepsilon_0 ^ \omega} </math>
|-
|<math>(0)(1)(2)(1)(1)(2)(0)(1)(2)(1)(1)(0)(1)(2)(1)(1)(2)</math>
|<math>\varepsilon_{\varepsilon_0 ^ {\varepsilon_0}} </math>
|-
|<math>(0)(1)(2)(1)(1)(2)(0)(1)(2)(1)(1)(2)</math>
|<math>\varepsilon_{\varepsilon_1} </math>
|-
|<math>(0)(1)(2)(1)(1)(2)(1)</math>
|<math>\varepsilon_{\varepsilon_\omega} </math>
|-
|<math>(0)(1)(2)(1)(1)(2)(1)(1)(2)</math>
|<math>\varepsilon_{\varepsilon_{\varepsilon_0}}</math>
|-
|<math>(0)(1)(2)(1)(2)</math>
|<math>\zeta_0 </math>
|-
|<math>(0)(1)(2)(1)(2)</math>
|<math>\zeta_0 </math>
|-
|<math>(0)(1)(2)(1)(2)(0)(1)(0)(1)(2)(1)(2)</math>
|<math>\zeta_0 ^2</math>
|-
|<math>(0)(1)(2)(1)(2)(0)(1)(1)</math>
|<math>\zeta_0 ^\omega</math>
|-
|<math>(0)(1)(2)(1)(2)(0)(1)(1)(0)(1)(2)(1)(2)</math>
|<math>\zeta_0 ^{\zeta_0}</math>
|-
|<math>(0)(1)(2)(1)(2)(0)(1)(2)</math>
|<math>\varepsilon_{\zeta_0 +1}</math>
|-
|<math>(0)(1)(2)(1)(2)(0)(1)(2)</math>
|<math>\varepsilon_{\zeta_0 +1}</math>
|-
|<math>(0)(1)(2)(1)(2)(0)(1)(2)(0)(1)(2)(1)(1)(2)</math>
|<math>\varepsilon_{\zeta_0 +\varepsilon_0}</math>
|-
|<math>(0)(1)(2)(1)(2)(0)(1)(2)(1)</math>
|<math>\varepsilon_{\zeta_0 \times \omega}</math>
|-
|<math>(0)(1)(2)(1)(2)(0)(1)(2)(1)(0)(1)(2)(1)(2)</math>
|<math>\varepsilon_{\zeta_0 ^2}</math>
|-
|<math>(0)(1)(2)(1)(2)(0)(1)(2)(1)(1)(0)(1)(2)(1)(2)</math>
|<math>\varepsilon_{\zeta_0 ^{\zeta_0}}</math>
|-
|<math>(0)(1)(2)(1)(2)(0)(1)(2)(1)(1)(2)</math>
|<math>\varepsilon_{\varepsilon_{\zeta_0 +1}}</math>
|-
|<math>(0)(1)(2)(1)(2)(0)(1)(2)(1)(2)</math>
|<math>\zeta_1</math>
|-
|<math>(0)(1)(2)(1)(2)(1)</math>
|<math>\zeta_\omega</math>
|-
|<math>(0)(1)(2)(1)(2)(1)(1)(2)</math>
|<math>\zeta_{\varepsilon_0}</math>
|-
|<math>(0)(1)(2)(1)(2)(1)(1)(2)(1)(2)</math>
|<math>\zeta_{\zeta_0}</math>
|-
|<math>(0)(1)(2)(1)(2)(1)(2)</math>
|<math>\eta_0</math>
|-
|<math>(0)(1)(2)(1)(2)(1)(2)(0)(1)(2)</math>
|<math>\varepsilon_{\eta_0+1}</math>
|-
|<math>(0)(1)(2)(1)(2)(1)(2)(0)(1)(2)(1)(2)</math>
|<math>\zeta_{\eta_0+1}</math>
|-
|<math>(0)(1)(2)(1)(2)(1)(2)(0)(1)(2)(1)(2)(1)(2)</math>
|<math>\eta_1</math>
|-
|<math>(0)(1)(2)(1)(2)(1)(2)(1)</math>
|<math>\eta_\omega</math>
|-
|<math>(0)(1)(2)(1)(2)(1)(2)(1)(1)(2)(1)(2)(1)(2)</math>
|<math>\eta_{\eta_0}</math>
|-
|<math>(0)(1)(2)(1)(2)(1)(2)(1)(2)</math>
|<math>\varphi(4,0)</math>
|-
|<math>(0)(1)(2)(2)</math>
|<math>\varphi(\omega,0)</math>
|-
|<math>(0)(1)(2)(2)(0)(1)(2)</math>
|<math>\varphi(1,\varphi(\omega,0)+1)</math>
|-
|<math>(0)(1)(2)(2)(0)(1)(2)(2)</math>
|<math>\varphi(\omega,1)</math>
|-
|<math>(0)(1)(2)(2)(1)</math>
|<math>\varphi(\omega,\omega)</math>
|-
|<math>(0)(1)(2)(2)(1)(1)(2)</math>
|<math>\varphi(\omega,\varepsilon_0)</math>
|-
|<math>(0)(1)(2)(2)(1)(1)(2)(1)(2)(2)</math>
|<math>\varphi(\omega,\varphi(\omega,0))</math>
|-
|<math>(0)(1)(2)(2)(1)(2)</math>
|<math>\varphi(\omega+1,0)</math>
|-
|<math>(0)(1)(2)(2)(1)(2)(1)(2)(2)</math>
|<math>\varphi(\omega\times 2,0)</math>
|-
|<math>(0)(1)(2)(2)(1)(2)(2)</math>
|<math>\varphi(\omega^2,0)</math>
|-
|<math>(0)(1)(2)(2)(2)</math>
|<math>\varphi(\omega^\omega,0)</math>
|-
|<math>(0)(1)(2)(3)</math>
|<math>\varphi(\varepsilon_0,0)</math>
|-
|<math>(0)(1)(2)(3)(1)(2)(3)</math>
|<math>\varphi(\varepsilon_1,0)</math>
|-
|<math>(0)(1)(2)(3)(2)(3)</math>
|<math>\varphi(\zeta_0,0)</math>
|-
|<math>(0)(1)(2)(3)(3)</math>
|<math>\varphi(\varphi(\omega,0),0)</math>
|-
|<math>(0)(1)(2)(3)(4)</math>
|<math>\varphi(\varphi(\varepsilon_0,0),0)</math>
|-
|<math>(0,0)(1,1)</math>
|<math>\varphi(1,0,0)</math>
|}

=== Part 3 ===
{| class="wikitable"
!BHM
!Veblen 函数
|-
|<math>(0,0)(1,1)(0,0)</math>
|<math>\varphi(1,0,0)+1</math>
|-
|<math>(0,0)(1,1)(0,0)(0,0)(1,1)</math>
|<math>\varphi(1,0,0)\times2</math>
|-
|<math>(0,0)(1,1)(0,0)(1,0)</math>
|<math>\omega^{\varphi(1,0,0)+1}</math>
|-
|<math>(0,0)(1,1)(0,0)(1,0)(1,0)</math>
|<math>\omega^{\omega^{\varphi(1,0,0)+1}}</math>
|-
|<math>(0,0)(1,1)(0,0)(1,0)(2,0)</math>
|<math>\varphi(1,\varphi(1,0,0)+1)</math>
|-
|<math>(0,0)(1,1)(0,0)(1,0)(2,0)(0,0)(1,1)</math>
|<math>\varphi(1,\varphi(1,0,0)\times2)</math>
|-
|<math>(0,0)(1,1)(0,0)(1,0)(2,0)(1,0)(1,0)(2,0)</math>
|<math>\varphi(1,\varphi(1,\varphi(1,0,0)+1))</math>
|-
|<math>(0,0)(1,1)(0,0)(1,0)(2,0)(1,0)(2,0)</math>
|<math>\varphi(2,\varphi(1,0,0)+1)</math>
|-
|<math>(0,0)(1,1)(0,0)(1,0)(2,0)(2,0)</math>
|<math>\varphi(\omega,\varphi(1,0,0)+1)</math>
|-
|<math>(0,0)(1,1)(0,0)(1,0)(2,0)(2,0)(1,0)(2,0)</math>
|<math>\varphi(\omega+1,\varphi(1,0,0)+1)</math>
|-
|<math>(0,0)(1,1)(0,0)(1,0)(2,0)(2,0)(1,0)(2,0)(2,0)</math>
|<math>\varphi(\omega^2,\varphi(1,0,0)+1)</math>
|-
|<math>(0,0)(1,1)(0,0)(1,0)(2,0)(2,0)(2,0)</math>
|<math>\varphi(\omega^\omega,\varphi(1,0,0)+1)</math>
|-
|<math>(0,0)(1,1)(0,0)(1,0)(2,0)(3,0)</math>
|<math>\varphi(\varphi(1,0),\varphi(1,0,0)+1)</math>
|-
|<math>(0,0)(1,1)(0,0)(1,0)(2,0)(3,0)(4,0)</math>
|<math>\varphi(\varphi(\varphi(1,0),0),\varphi(1,0,0)+1)</math>
|-
|<math>(0,0)(1,1)(0,0)(1,0)(2,0)(3,0)(4,0)(5,0)</math>
|<math>\varphi (\varphi (\varphi(\varphi(1,0),0),0),\varphi(1,0,0)+1)</math>
|-
|<math>(0,0)(1,1)(0,0)(1,1)</math>
|<math>\varphi(\varphi(1,0,0),1)</math>
|-
|<math>(0,0)(1,1)(0,0)(1,1)(0,0)(1,1)</math>
|<math>\varphi(\varphi(1,0,0),2)</math>
|-
|<math>(0,0)(1,1)(1,0)</math>
|<math>\varphi(\varphi(1,0,0),\omega)</math>
|-
|<math>(0,0)(1,1)(1,0)(0,0)(1,1)</math>
|<math>\varphi(\varphi(1,0,0),\omega+1)</math>
|-
|<math>(0,0)(1,1)(1,0)(0,0)(1,1)(0,0)(1,1)(1,0)</math>
|<math>\varphi(\varphi(1,0,0),\omega\times2)</math>
|-
|<math>(0,0)(1,1)(1,0)(0,0)(1,1)(1,0)</math>
|<math>\varphi(\varphi(1,0,0),\omega^2)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)</math>
|<math>\varphi(\varphi(1,0,0),\omega^\omega)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(1,0)</math>
|<math>\varphi(\varphi(1,0,0),\omega^{\omega^\omega})</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)</math>
|<math>\varphi(\varphi(1,0,0),\varphi(1,0))</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(1,0)(2,0)</math>
|<math>\varphi(\varphi(1,0,0),\varphi(2,0))</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(2,0)</math>
|<math>\varphi(\varphi(1,0,0),\varphi(\omega,0))</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,0)</math>
|<math>\varphi(\varphi(1,0,0),\varphi(\varphi(1,0),0))</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,0)(4,0)</math>
|<math>\varphi(\varphi(1,0,0),\varphi(\varphi(\varphi(1,0),0),0))</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)</math>
|<math>\varphi(\varphi(1,0,0),\varphi(1,0,0))</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(0,0)(1,1)</math>
|<math>\varphi(\varphi(1,0,0),\varphi(1,0,0)+1)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(0,0)(1,1)(0,0)(1,1)</math>
|<math>\varphi(\varphi(1,0,0),\varphi(1,0,0)+2)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(0,0)(1,1)(0,0)(1,1)(1,0)</math>
|<math>\varphi(\varphi(1,0,0),\varphi(1,0,0)+\omega)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(0,0)(1,1)(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)</math>
|<math>\varphi(\varphi(1,0,0),\varphi(1,0,0)\times2)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(0,0)(1,1)(1,0)</math>
|<math>\varphi(\varphi(1,0,0),\omega^{\varphi(1,0,0)+1})</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(0,0)(1,1)(1,0)(1,0)(2,0)</math>
|<math>\varphi(\varphi(1,0,0),\varphi(1,\varphi(1,0,0)+1))</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(0,0)(1,1)(1,0)(1,0)(2,0)(1,0)(2,0)</math>
|<math>\varphi(\varphi(1,0,0),\varphi(2,\varphi(1,0,0)+1))</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(0,0)(1,1)(1,0)(1,0)(2,0)(2,0)</math>
|<math>\varphi(\varphi(1,0,0),\varphi(\omega,\varphi(1,0,0)+1))</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(0,0)(1,1)(1,0)(1,0)(2,0)(3,0)</math>
|<math>\varphi(\varphi(1,0,0),\varphi(\varphi(1,0),\varphi(1,0,0)+1))</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)</math>
|<math>\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0),1))</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)</math>
|<math>\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0),\omega))</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)</math>
|<math>\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0),\omega+1))</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(1,0)</math>
|<math>\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0),\omega^\omega))</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(1,0)(2,0)</math>
|<math>\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0),\varphi(1,0)))</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(1,0)(2,0)(2,0)</math>
|<math>\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0),\varphi(\omega,0)))</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(1,0)(2,0)(3,1)</math>
|<math>\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0),\varphi(1,0,0)))</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(1,0)(2,0)(3,1)(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(1,0)(2,0)(3,1)</math>
|<math>\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0),1)))</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)</math>
|<math>\varphi(\varphi(1,0,0)+1,0)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)(0,0)(1,1)</math>
|<math>\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0)+1,0)+1)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)(0,0)(1,1)(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)</math>
|<math>\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0)+1,0)\times2)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)(0,0)(1,1)(1,0)</math>
|<math>\varphi(\varphi(1,0,0),\omega^{\varphi(\varphi(1,0,0)+1,0)+1})</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)(0,0)(1,1)(1,0)(1,0)(2,0)</math>
|<math>\varphi(\varphi(1,0,0),\varphi(1,\varphi(\varphi(1,0,0)+1,0)+1))</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)</math>
|<math>\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0)+1,0)+1))</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)</math>
|<math>\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0)+1,0)\times2))</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(1,0)(2,0)</math>
|<math>\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0),\varphi(1,\varphi(\varphi(1,0,0)+1,0)+1)))</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(1,0)(2,0)(3,1)</math>
|<math>\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0)+1,0)+1)))</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)</math>
|<math>\varphi(\varphi(1,0,0)+1,1)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)(1,0)</math>
|<math>\varphi(\varphi(1,0,0)+1,\omega)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)(1,0)(1,0)(2,0)</math>
|<math>\varphi(\varphi(1,0,0)+1,\varphi(1,0))</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)(1,0)(1,0)(2,0)(3,1)</math>
|<math>\varphi(\varphi(1,0,0)+1,\varphi(1,0,0))</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)</math>
|<math>\varphi(\varphi(1,0,0)+1,\varphi(\varphi(1,0,0)+1,0))</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)(1,0)(2,0)</math>
|<math>\varphi(\varphi(1,0,0)+2,0)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)(1,0)(2,0)(2,0)</math>
|<math>\varphi(\varphi(1,0,0)+\omega,0)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)(1,0)(2,0)(3,0)</math>
|<math>\varphi(\varphi(1,0,0)+\varphi(1,0),0)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)(1,0)(2,0)(3,1)</math>
|<math>\varphi(\varphi(1,0,0)\times2,0)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)(1,0)(2,0)(3,1)(1,0)(2,0)(1,0)(2,0)(3,1)</math>
|<math>\varphi(\varphi(1,0,0)\times3,0)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)(2,0)</math>
|<math>\varphi(\omega^{\varphi(1,0,0)+1},0)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)(3,0)</math>
|<math>\varphi(\varphi(1,\varphi(1,0,0)+1),0)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)(3,1)</math>
|<math>\varphi(\varphi(\varphi(1,0,0),1),0)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)(3,1)(1,0)(2,0)</math>
|<math>\varphi(\varphi(\varphi(1,0,0),1)+1,0)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)(3,1)(1,0)(2,0)(2,0)</math>
|<math>\varphi(\omega^{\varphi(\varphi(1,0,0),1)+1},0)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)(3,1)(1,0)(2,0)(3,0)</math>
|<math>\varphi(\varphi(1,\varphi(\varphi(1,0,0),1)+1),0)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)(3,1)(1,0)(2,0)(3,1)</math>
|<math>\varphi(\varphi(\varphi(1,0,0),2),0)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(2,0)</math>
|<math>\varphi(\varphi(\varphi(1,0,0),\omega),0)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(2,0)(1,0)(2,0)(3,1)</math>
|<math>\varphi(\varphi(\varphi(1,0,0),\omega+1),0)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(2,0)(1,0)(2,0)(3,1)(1,0)(2,0)(3,1)(2,0)</math>
|<math>\varphi(\varphi(\varphi(1,0,0),\omega\times2),0)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(2,0)(2,0)</math>
|<math>\varphi(\varphi(\varphi(1,0,0),\omega^\omega),0)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(2,0)(2,0)(3,0)</math>
|<math>\varphi(\varphi(\varphi(1,0,0),\varphi(1,0)),0)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(2,0)(2,0)(3,1)</math>
|<math>\varphi(\varphi(\varphi(1,0,0),\varphi(1,0,0)),0)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(2,0)(2,0)(3,1)(1,0)(2,0)(3,1)</math>
|<math>\varphi(\varphi(\varphi(1,0,0),\varphi(1,0,0)+1),0)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(2,0)(2,0)(3,1)(1,0)(2,0)(3,1)(2,0)</math>
|<math>\varphi(\varphi(\varphi(1,0,0),\omega^{\varphi(1,0,0)+1}),0)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(2,0)(2,0)(3,1)(1,0)(2,0)(3,1)(2,0)(2,0)(3,0)</math>
|<math>\varphi(\varphi(\varphi(1,0,0),\varphi(1,\varphi(1,0,0)+1)),0)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(2,0)(2,0)(3,1)(1,0)(2,0)(3,1)(2,0)(2,0)(3,1)</math>
|<math>\varphi(\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0),1)),0)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(2,0)(2,0)(3,1)(2,0)</math>
|<math>\varphi(\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0),\omega)),0)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(2,0)(2,0)(3,1)(2,0)(2,0)(3,1)</math>
|<math>\varphi(\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0),\varphi(1,0,0))),0)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(2,0)(3,0)</math>
|<math>\varphi(\varphi(\varphi(1,0,0)+1,0),0)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(2,0)(3,0)(2,0)(3,0)</math>
|<math>\varphi(\varphi(\varphi(1,0,0)+2,0),0)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(2,0)(3,0)(2,0)(3,1)</math>
|<math>\varphi(\varphi(\varphi(1,0,0)\times2,0),0)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(2,0)(3,0)(3,0)</math>
|<math>\varphi(\varphi(\omega^{\varphi(1,0,0)+1},0),0)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(2,0)(3,1)</math>
|<math>\varphi(\varphi(\varphi(\varphi(1,0,0),1),0),0)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(3,0)</math>
|<math>\varphi(\varphi(\varphi(\varphi(1,0,0),\omega),0),0)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(3,0)(3,0)(4,0)</math>
|<math>\varphi(\varphi(\varphi(\varphi(1,0,0),\varphi(1,0)),0),0)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(3,0)(3,0)(4,0)(5,1)</math>
|<math>\varphi(\varphi(\varphi(\varphi(1,0,0),\varphi(1,0,0)),0),0)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(3,0)(3,0)(4,0)(5,1)(2,0)(3,1)</math>
|<math>\varphi(\varphi(\varphi(\varphi(1,0,0),\varphi(1,0,0)+1),0),0)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(3,0)(3,0)(4,0)(5,1)(2,0)(3,1)(3,0)(3,0)(4,0)(5,1)</math>
|<math>\varphi(\varphi(\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0),1)),0),0)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(3,0)(3,0)(4,0)(5,1)(3,0)</math>
|<math>\varphi(\varphi(\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0),\omega)),0),0)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(3,0)(3,0)(4,0)(5,1)(3,0)(4,0)</math>
|<math>\varphi(\varphi(\varphi(\varphi(1,0,0)+1,0),0),0)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(3,0)(3,0)(4,0)(5,1)(3,0)(4,0)(5,0)</math>
|<math>\varphi(\varphi(\varphi(\varphi(1,\varphi(1,0,0)+1),0),0),0)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(3,0)(3,0)(4,0)(5,1)(3,0)(4,0)(5,1)</math>
|<math>\varphi(\varphi(\varphi(\varphi(\varphi(1,0,0),1),0),0),0)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(3,0)(3,0)(4,0)(5,1)(4,0)(5,1)</math>
|<math>\varphi(\varphi(\varphi(\varphi(\varphi(\varphi(1,0,0),1),0),0),0),0)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,1)</math>
|<math>\varphi(1,0,1)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,1)(0,0)(1,1)</math>
|<math>\varphi(\varphi(1,0,0),\varphi(1,0,1)+1)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,1)(0,0)(1,1)(1,0)</math>
|<math>\varphi(\varphi(1,0,0),\omega^{\varphi(1,0,1)+1})</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,1)(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)</math>
|<math>\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0),\varphi(1,0,1)+1))</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,1)(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)</math>
|<math>\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0),\varphi(1,0,1)+2))</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,1)(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(2,0)</math>
|<math>\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0),\varphi(1,0,1)+\omega))</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,1)(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(0,0)(1,1)(1,0)(1,0)(2,1)</math>
|<math>\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0),\varphi(1,0,1)\times2))</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,1)(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)</math>
|<math>\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0),\omega^{\varphi(1,0,1)+1}))</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,1)(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(1,0)(2,1)(3,1)</math>
|<math>\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0),\varphi(1,0,1)+1)))</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,1)(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)</math>
|<math>\varphi(\varphi(1,0,0)+1,\varphi(1,0,1)+1)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,1)(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)(1,0)(2,0)(3,1)</math>
|<math>\varphi(\varphi(1,0,0)\times2,\varphi(1,0,1)+1)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,1)(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)(3,1)</math>
|<math>\varphi(\varphi(\varphi(1,0,0),1),\varphi(1,0,1)+1)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,1)(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(2,0)(3,1)</math>
|<math>\varphi(\varphi(\varphi(\varphi(1,0,0),1),0),\varphi(1,0,1)+1)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,1)(0,0)(1,1)(1,0)(1,0)(2,1)</math>
|<math>\varphi(\varphi(1,0,1),1)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,1)(1,0)</math>
|<math>\varphi(\varphi(1,0,1),\omega)</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,1)(1,0)(1,0)(2,0)</math>
|<math>\varphi(\varphi(1,0,1),\varphi(1,0))</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,1)(1,0)(1,0)(2,0)(3,1)</math>
|<math>\varphi(\varphi(1,0,1),\varphi(1,0,0))</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,1)(1,0)(1,0)(2,0)(3,1)(0,0)(1,1)(1,0)(1,0)(2,1)(1,0)(1,0)(2,0)(3,1)</math>
|<math>\varphi(\varphi(1,0,1),\varphi(\varphi(1,0,0),1))</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,1)(1,0)(1,0)(2,0)(3,1)(1,0)</math>
|<math>\varphi(\varphi(1,0,1),\varphi(\varphi(1,0,0),\omega))</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,1)(1,0)(1,0)(2,0)(3,1)(1,0)(1,0)(2,0)(3,1)</math>
|<math>\varphi(\varphi(1,0,1),\varphi(\varphi(1,0,0),\varphi(1,0,0)))</math>
|-
|<math>(0,0)(1,1)(1,0)(1,0)(2,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)</math>
|<math>\varphi(\varphi(1,0,1),\varphi(\varphi(1,0,0)+1,0))</math>
|}
[[分类:分析]]