打开/关闭菜单
打开/关闭外观设置菜单
打开/关闭个人菜单
未登录
未登录用户的IP地址会在进行任意编辑后公开展示。

BMS分析:修订间差异

来自Googology Wiki
Tabelog留言 | 贡献
无编辑摘要
Z留言 | 贡献
无编辑摘要
 
(未显示同一用户的5个中间版本)
第1行: 第1行:
目前使用的 OCF 为 M 型,后续补充 BOCF
本条目展示的分析来自最菜萌新


==== Part 1:单行 BMS(PrSS) ====
== Part 1:0~[[BO]] ==
<math>\varnothing=0</math>
主词条:[[BMS分析Part1:0~BO|BMS分析Part1:0~BO]]


<math>(0)=1</math>
这个部分的BMS行为较为简单。


<math>(0)(0)=2</math>
== Part 2:[[BO]]~[[EBO]] ==
由于提升效应的出现,三行之后 BMS 的行为复杂度急剧上升。


<math>(0)(0)(0)=3</math>
主词条:[[BMS分析Part2:BO~EBO]]


<math>(0)(1)=(0)(0)(0)(0)(0)...=\omega</math>
== Part 3:EBO~[[SSO]] ==
在这里,我们将正式引入[[投影序数]]。


<math>(0)(1)(0)=\omega+1</math>
主词条:[[BMS分析Part3:EBO~SSO]]


<math>(0)(1)(0)(0)=\omega+2</math>
== Part4:SSO~[[LRO|pLRO]] ==
在我们的努力之下,一个“升级版”的BO浮出了水面。


<math>(0)(1)(0)(1)=\omega\times2</math>
主词条:[[BMS分析Part4:SSO~pLRO]]


<math>(0)(1)(0)(1)(0)(1)=\omega\times3</math>
== Part5:pLRO~TSSO ==
在投影序数的助力下,我们抵达了三行BMS的终点,抵达了可怕与不可怕的分界点。


<math>(0)(1)(1)=(0)(1)(0)(1)(0)(1)...=\omega^2</math>
主词条:[[BMS分析Part5:pLRO~TSSO]]


<math>(0)(1)(1)(0)=\omega^2+1</math>
== Part6:TSSO~SHO ==
[[向上投影]]为我们揭示了BMS的<math>\varepsilon_0</math>结构


<math>(0)(1)(1)(0)(1)=\omega^2+\omega</math>
主词条:[[BMS分析Part6]]、[[BMS分析Part7]]
 
<math>(0)(1)(1)(0)(1)(0)(1)=\omega^2+\omega\times2</math>
 
<math>(0)(1)(1)(0)(1)(1)=\omega^2\times2</math>
 
<math>(0)(1)(1)(0)(1)(1)(0)(1)=\omega^2\times2+\omega</math>
 
<math>(0)(1)(1)(0)(1)(1)(0)(1)(1)=\omega^2\times3</math>
 
<math>(0)(1)(1)(1)=\omega^3</math>
 
<math>(0)(1)(1)(1)(1)=\omega^4</math>
 
<math>(0)(1)(2)=(0)(1)(1)(1)(1)...=\omega^\omega</math>
 
<math>(0)(1)(2)(0)(1)(2)=\omega^\omega\times2</math>
 
<math>(0)(1)(2)(1)=\omega^{\omega+1}</math>
 
<math>(0)(1)(2)(1)(1)=\omega^{\omega+2}</math>
 
<math>(0)(1)(2)(1)(1)(1)=\omega^{\omega+3}</math>
 
<math>(0)(1)(2)(1)(2)=\omega^{\omega\times2}</math>
 
<math>(0)(1)(2)(1)(2)(1)(2)=\omega^{\omega\times3}</math>
 
<math>(0)(1)(2)(2)=\omega^{\omega^2}</math>
 
<math>(0)(1)(2)(2)(1)=\omega^{\omega^2+1}</math>
 
<math>(0)(1)(2)(2)(1)(2)=\omega^{\omega^2+\omega}</math>
 
<math>(0)(1)(2)(2)(1)(2)(2)=\omega^{\omega^2\times2}</math>
 
<math>(0)(1)(2)(2)(1)(2)(2)(1)(2)(2)=\omega^{\omega^2\times3}</math>
 
<math>(0)(1)(2)(2)(2)=\omega^{\omega^3}</math>
 
<math>(0)(1)(2)(2)(2)(2)=\omega^{\omega^4}</math>
 
<math>(0)(1)(2)(3)=(0)(1)(2)(2)(2)(2)...=\omega^{\omega^\omega}</math>
 
<math>(0)(1)(2)(3)(4)=\omega^{\omega^{\omega^\omega}}</math>
 
<math>(0)(1)(2)(3)(4)(5)=\omega^{\omega^{\omega^{\omega^\omega}}}</math>
 
<math>(0)(1,1)=(0)(1)(2)(3)(4)(5)(6)...=\varepsilon_0</math>
 
==== Part 2:双行 BMS ====
{| class="wikitable"
|-
! BMS !! Veblen !! MOCF
|-
| <math>(0)(1,1)</math>|| <math>\varepsilon_0</math>
|-
| <math>(0)(1,1)(0,0)</math>|| <math>\varepsilon_0+1</math>
|-
| <math>(0)(1,1)(0,0)(1,0)</math>|| <math>\varepsilon_0+\omega</math>
|-
| <math>(0)(1,1)(0,0)(1,1)</math>|| <math>\varepsilon_0\times2</math>
|-
| <math>(0)(1,1)(0,0)(1,1)(0,0)(1,1)</math>|| <math>\varepsilon_0\times3</math>
|-
| <math>(0)(1,1)(1,0)</math>|| <math>\varepsilon_0\times\omega</math>
|-
| <math>(0)(1,1)(1,0)(1,0)</math>|| <math>\varepsilon_0\times\omega^2</math>
|-
| <math>(0)(1,1)(1,0)(2,0)</math>|| <math>\varepsilon_0\times\omega^\omega</math>
|-
| <math>(0)(1,1)(1,0)(2,0)(3,0)</math>|| <math>\varepsilon_0\times\omega^{\omega^\omega}</math>
|-
| <math>(0)(1,1)(1,0)(2,1)</math>|| <math>\varepsilon_0^2</math>
|-
| <math>(0)(1,1)(1,0)(2,1)(1,0)(2,0)</math>|| <math>\varepsilon_0^2\times\omega</math>
|-
| <math>(0)(1,1)(1,0)(2,1)(1,0)(2,0)(3,0)</math>|| <math>\varepsilon_0^2\times\omega^\omega</math>
|-
| <math>(0)(1,1)(1,0)(2,1)(1,0)(2,1)</math>|| <math>\varepsilon_0^3</math>
|-
| <math>(0)(1,1)(1,0)(2,1)(1,0)(2,1)(1,0)(2,1)</math>|| <math>\varepsilon_0^4</math>
|-
| <math>(0)(1,1)(1,0)(2,1)(2,0)</math>|| <math>\varepsilon_0^\omega</math>
|-
| <math>(0)(1,1)(1,0)(2,1)(2,0)(1,0)(2,1)</math>|| <math>\varepsilon_0^{\omega+1}</math>
|-
| <math>(0)(1,1)(1,0)(2,1)(2,0)(1,0)(2,1)(1,0)(2,1)</math>|| <math>\varepsilon_0^{\omega+2}</math>
|-
| <math>(0)(1,1)(1,0)(2,1)(2,0)(1,0)(2,1)(2,0)</math>|| <math>\varepsilon_0^{\omega\times2}</math>
|-
| <math>(0)(1,1)(1,0)(2,1)(2,0)(1,0)(2,1)(2,0)(1,0)(2,1)(2,0)</math>|| <math>\varepsilon_0^{\omega\times3}</math>
|-
| <math>(0)(1,1)(1,0)(2,1)(2,0)(2,0)</math>|| <math>\varepsilon_0^{\omega^2}</math>
|-
| <math>(0)(1,1)(1,0)(2,1)(2,0)(3,0)</math>|| <math>\varepsilon_0^{\omega^\omega}</math>
|-
| <math>(0)(1,1)(1,0)(2,1)(2,0)(3,0)(4,0)</math>|| <math>\varepsilon_0^{\omega^{\omega^\omega}}</math>
|-
| <math>(0)(1,1)(1,0)(2,1)(2,0)(3,1)</math>|| <math>\varepsilon_0^{\varepsilon_0}</math>
|-
| <math>(0)(1,1)(1,0)(2,1)(2,0)(3,1)(3,0)(4,1)</math>|| <math>\varepsilon_0^{\varepsilon_0^{\varepsilon_0}}</math>
|-
| <math>(0)(1,1)(1,0)(2,1)(2,0)(3,1)(3,0)(4,1)(4,0)(5,1)</math>|| <math>\varepsilon_0^{\varepsilon_0^{\varepsilon_0^{\varepsilon_0}}}</math>
|-
| <math>(0)(1,1)(1,1)</math>|| <math>\varepsilon_1</math>
|-
| <math>(0)(1,1)(1,1)(0,0)(1,1)(1,1)</math>|| <math>\varepsilon_1\times2</math>
|-
| <math>(0)(1,1)(1,1)(1,0)</math>|| <math>\varepsilon_1\times\omega</math>
|-
| <math>(0)(1,1)(1,1)(1,0)(2,1)</math>|| <math>\varepsilon_1\times\varepsilon_0</math>
|-
| <math>(0)(1,1)(1,1)(1,0)(2,1)(2,0)(3,1)</math>|| <math>\varepsilon_1\times\varepsilon_0^2</math>
|-
| <math>(0)(1,1)(1,1)(1,0)(2,1)(2,0)(3,1)(3,0)(4,1)</math>|| <math>\varepsilon_1\times\varepsilon_0^{\varepsilon_0}</math>
|-
| <math>(0)(1,1)(1,1)(1,0)(2,1)(2,1)</math>|| <math>\varepsilon_1^2</math>
|-
| <math>(0)(1,1)(1,1)(1,0)(2,1)(2,1)(2,0)</math>|| <math>\varepsilon_1^\omega</math>
|-
| <math>(0)(1,1)(1,1)(1,0)(2,1)(2,1)(2,0)(3,1)</math>|| <math>\varepsilon_1^{\varepsilon_0}</math>
|-
| <math>(0)(1,1)(1,1)(1,0)(2,1)(2,1)(2,0)(3,1)(3,1)</math>|| <math>\varepsilon_1^{\varepsilon_1}</math>
|-
| <math>(0)(1,1)(1,1)(1,0)(2,1)(2,1)(2,0)(3,1)(3,1)(3,0)(4,1)(4,1)</math>|| <math>\varepsilon_1^{\varepsilon_1^{\varepsilon_1}}</math>
|-
| <math>(0)(1,1)(1,1)(1,1)</math>|| <math>\varepsilon_2</math>
|-
| <math>(0)(1,1)(1,1)(1,1)(1,1)</math>|| <math>\varepsilon_3</math>
|-
| <math>(0)(1,1)(2,0)</math>|| <math>\varepsilon_\omega</math>
|-
| <math>(0)(1,1)(2,0)(1,0)</math>|| <math>\varepsilon_\omega\times\omega</math>
|-
| <math>(0)(1,1)(2,0)(1,0)(2,1)</math>|| <math>\varepsilon_\omega\times\varepsilon_0</math>
|-
| <math>(0)(1,1)(2,0)(1,0)(2,1)(2,1)</math>|| <math>\varepsilon_\omega\times\varepsilon_1</math>
|-
| <math>(0)(1,1)(2,0)(1,0)(2,1)(2,1)(2,1)</math>|| <math>\varepsilon_\omega\times\varepsilon_2</math>
|-
| <math>(0)(1,1)(2,0)(1,0)(2,1)(2,1)(2,1)(2,1)</math>|| <math>\varepsilon_\omega\times\varepsilon_3</math>
|-
| <math>(0)(1,1)(2,0)(1,0)(2,1)(3,0)</math>|| <math>\varepsilon_\omega^2</math>
|-
| <math>(0)(1,1)(2,0)(1,0)(2,1)(3,0)(2,0)(3,1)(4,0)</math>|| <math>\varepsilon_\omega^{\varepsilon_\omega}</math>
|-
| <math>(0)(1,1)(2,0)(1,1)</math>|| <math>\varepsilon_{\omega+1}</math>
|-
| <math>(0)(1,1)(2,0)(1,1)(1,1)</math>|| <math>\varepsilon_{\omega+2}</math>
|-
| <math>(0)(1,1)(2,0)(1,1)(1,1)(1,1)</math>|| <math>\varepsilon_{\omega+3}</math>
|-
| <math>(0)(1,1)(2,0)(1,1)(2,0)</math>|| <math>\varepsilon_{\omega\times2}</math>
|-
| <math>(0)(1,1)(2,0)(1,1)(2,0)(1,1)(2,0)</math>|| <math>\varepsilon_{\omega\times3}</math>
|-
| <math>(0)(1,1)(2,0)(2,0)</math>|| <math>\varepsilon_{\omega^2}</math>
|-
| <math>(0)(1,1)(2,0)(2,0)(2,0)</math>|| <math>\varepsilon_{\omega^3}</math>
|-
| <math>(0)(1,1)(2,0)(3,0)</math>|| <math>\varepsilon_{\omega^\omega}</math>
|-
| <math>(0)(1,1)(2,0)(3,0)(4,0)</math>|| <math>\varepsilon_{\omega^{\omega^\omega}}</math>
|-
| <math>(0)(1,1)(2,0)(3,1)</math>|| <math>\varepsilon_{\varepsilon_0}</math>
|-
| <math>(0)(1,1)(2,0)(3,1)(1,1)</math>|| <math>\varepsilon_{\varepsilon_0+1}</math>
|-
| <math>(0)(1,1)(2,0)(3,1)(3,1)</math>|| <math>\varepsilon_{\varepsilon_1}</math>
|-
| <math>(0)(1,1)(2,0)(3,1)(4,0)</math>|| <math>\varepsilon_{\varepsilon_\omega}</math>
|-
| <math>(0)(1,1)(2,0)(3,1)(4,0)(5,1)</math>|| <math>\varepsilon_{\varepsilon_{\varepsilon_0}}</math>
|-
| <math>(0)(1,1)(2,0)(3,1)(4,0)(5,1)(6,0)(7,1)</math>|| <math>\varepsilon_{\varepsilon_{\varepsilon_{\varepsilon_0}}}</math>
|-
| <math>(0)(1,1)(2,1)</math>|| <math>\zeta_0</math>
|-
| <math>(0)(1,1)(2,1)(1,0)(2,1)(3,1)</math>|| <math>\zeta_0^2</math>
|-
| <math>(0)(1,1)(2,1)(1,0)(2,1)(3,1)(2,0)(3,1)(4,1)</math>|| <math>\zeta_0^{\zeta_0}</math>
|-
| <math>(0)(1,1)(2,1)(1,1)</math>|| <math>\varepsilon_{\zeta_0+1}</math>
|-
| <math>(0)(1,1)(2,1)(1,1)(1,0)(2,1)(3,1)(2,1)</math>|| <math>\varepsilon_{\zeta_0+1}^2</math>
|-
| <math>(0)(1,1)(2,1)(1,1)(1,1)</math>|| <math>\varepsilon_{\zeta_0+2}</math>
|-
| <math>(0)(1,1)(2,1)(1,1)(2,0)</math>|| <math>\varepsilon_{\zeta_0+\omega}</math>
|-
| <math>(0)(1,1)(2,1)(1,1)(2,0)(3,1)</math>|| <math>\varepsilon_{\zeta_0+\varepsilon_0}</math>
|-
| <math>(0)(1,1)(2,1)(1,1)(2,0)(3,1)(4,1)</math>|| <math>\varepsilon_{\zeta_0\times2}</math>
|-
| <math>(0)(1,1)(2,1)(1,1)(2,0)(3,1)(4,1)(3,1)</math>|| <math>\varepsilon_{\varepsilon_{\zeta_0+1}}</math>
|-
| <math>(0)(1,1)(2,1)(1,1)(2,0)(3,1)(4,1)(3,1)(4,0)(5,1)(6,1)(5,1)</math>|| <math>\varepsilon_{\varepsilon_{\varepsilon_{\zeta+1}}}</math>
|-
| <math>(0)(1,1)(2,1)(1,1)(2,1)</math>|| <math>\zeta_1</math>
|-
| <math>(0)(1,1)(2,1)(1,1)(2,1)(1,1)</math>|| <math>\varepsilon_{\zeta_1+1}</math>
|-
| <math>(0)(1,1)(2,1)(1,1)(2,0)</math>|| <math>\varepsilon_{\zeta_1+\omega}</math>
|-
| <math>(0)(1,1)(2,1)(1,1)(2,1)(1,1)(2,1)</math>|| <math>\zeta_2</math>
|-
| <math>(0)(1,1)(2,1)(1,1)(2,1)(1,1)(2,1)(1,1)(2,1)</math>|| <math>\zeta_3</math>
|-
| <math>(0)(1,1)(2,1)(2,0)</math>|| <math>\zeta_\omega</math>
|-
| <math>(0)(1,1)(2,1)(2,0)(2,0)</math>|| <math>\zeta_{\omega^2}</math>
|-
| <math>(0)(1,1)(2,1)(2,0)(3,1)</math>|| <math>\zeta_{\varepsilon_0}</math>
|-
| <math>(0)(1,1)(2,1)(2,0)(3,1)(4,1)</math>|| <math>\zeta_{\zeta_0}</math>
|-
| <math>(0)(1,1)(2,1)(2,0)(3,1)(4,1)(4,0)(5,1)(6,1)</math>|| <math>\zeta_{\zeta_{\zeta_0}}</math>
|-
| <math>(0)(1,1)(2,1)(2,1)</math>|| <math>\eta_0</math>
|-
| <math>(0)(1,1)(2,1)(2,1)(1,1)</math>|| <math>\varepsilon_{\eta_0+1}</math>
|-
| <math>(0)(1,1)(2,1)(2,1)(1,1)(2,1)</math>|| <math>\zeta_{\eta_0+1}</math>
|-
| <math>(0)(1,1)(2,1)(2,1)(1,1)(2,1)(2,0)(3,1)(4,1)(4,1)(3,1)(4,1)</math>|| <math>\zeta_{\zeta_{\eta_0+1}}</math>
|-
| <math>(0)(1,1)(2,1)(2,1)(1,1)(2,1)(2,1)</math>|| <math>\eta_1</math>
|-
| <math>(0)(1,1)(2,1)(2,1)(1,1)(2,1)(2,1)(1,1)(2,1)(2,1)</math>|| <math>\eta_2</math>
|-
| <math>(0)(1,1)(2,1)(2,1)(2,0)</math>|| <math>\eta_\omega</math>
|-
| <math>(0)(1,1)(2,1)(2,1)(2,1)</math>|| <math>\varphi(4,0)</math>|| <math>\psi(\Omega^3)</math>
|-
| <math>(0)(1,1)(2,1)(3,0)</math>|| <math>\varphi(\omega,0)</math>|| <math>\psi(\Omega^\omega)</math>
|-
| <math>(0)(1,1)(2,1)(3,0)(1,1)</math>|| <math>\varphi(1,\varphi(\omega,0)+1)</math>|| <math>\psi(\Omega^\omega+1)</math>
|-
| <math>(0)(1,1)(2,1)(3,0)(1,1)(2,1)</math>|| <math>\varphi(2,\varphi(\omega,0)+1)</math>|| <math>\psi(\Omega^\omega+\Omega)</math>
|-
| <math>(0)(1,1)(2,1)(3,0)(1,1)(2,1)(2,1)</math>|| <math>\varphi(3,\varphi(\omega,0)+1)</math>|| <math>\psi(\Omega^\omega+\Omega^2)</math>
|-
| <math>(0)(1,1)(2,1)(3,0)(1,1)(2,1)(3,0)</math>|| <math>\varphi(\omega,1)</math>|| <math>\psi(\Omega^\omega\times2)</math>
|-
| <math>(0)(1,1)(2,1)(3,0)(1,1)(2,1)(3,0)(1,1)(2,1)(3,0)</math>|| <math>\varphi(\omega,2)</math>|| <math>\psi(\Omega^\omega\times3)</math>
|-
| <math>(0)(1,1)(2,1)(3,0)(2,0)</math>|| <math>\varphi(\omega,\omega)</math>|| <math>\psi(\Omega^\omega\times\omega)</math>
|-
| <math>(0)(1,1)(2,1)(3,0)(2,1)</math>|| <math>\varphi(\omega+1,0)</math>|| <math>\psi(\Omega^{\omega+1})</math>
|-
| <math>(0)(1,1)(2,1)(3,0)(2,1)(2,1)</math>|| <math>\varphi(\omega+2,0)</math>|| <math>\psi(\Omega^{\omega+2})</math>
|-
| <math>(0)(1,1)(2,1)(3,0)(2,1)(2,1)(2,1)</math>|| <math>\varphi(\omega+3,0)</math>|| <math>\psi(\Omega^{\omega+3})</math>
|-
| <math>(0)(1,1)(2,1)(3,0)(2,1)(3,0)</math>|| <math>\varphi(\omega\times2,0)</math>|| <math>\psi(\Omega^{\omega\times2})</math>
|-
| <math>(0)(1,1)(2,1)(3,0)(2,1)(3,0)(2,1)(3,0)</math>|| <math>\varphi(\omega\times3,0)</math>|| <math>\psi(\Omega^{\omega\times3})</math>
|-
| <math>(0)(1,1)(2,1)(3,0)(3,0)</math>|| <math>\varphi(\omega^2,0)</math>|| <math>\psi(\Omega^{\omega^2})</math>
|-
| <math>(0)(1,1)(2,1)(3,0)(4,1)</math>|| <math>\varphi(\varphi(1,0),0)</math>|| <math>\psi(\Omega^{\psi(0)})</math>
|-
| <math>(0)(1,1)(2,1)(3,0)(4,1)(5,1)</math>|| <math>\varphi(\varphi(2,0),0)</math>|| <math>\psi(\Omega^{\psi(\Omega)})</math>
|-
| <math>(0)(1,1)(2,1)(3,0)(4,1)(5,1)(6,0)</math>|| <math>\varphi(\varphi(\omega,0),0)</math>|| <math>\psi(\Omega^{\psi(\Omega^\omega)})</math>
|-
| <math>(0)(1,1)(2,1)(3,0)(4,1)(5,1)(6,0)(7,1)(8,1)(9,0)</math>|| <math>\varphi(\varphi(\varphi(\omega,0),0),0)</math>|| <math>\psi(\Omega^{\psi(\Omega^{\psi(\Omega^\omega)})})</math>
|-
| <math>(0)(1,1)(2,1)(3,1)</math>|| <math>\varphi(1,0,0)=\Gamma_0</math>|| <math>\psi(\Omega^\Omega)</math>
|-
| <math>(0)(1,1)(2,1)(3,1)(1,1)(2,1)(3,1)</math>|| <math>\varphi(1,0,1)=\Gamma_1</math>|| <math>\psi(\Omega^\Omega\times2)</math>
|-
| <math>(0)(1,1)(2,1)(3,1)(1,1)(2,1)(3,1)(1,1)(2,1)(3,1)</math>|| <math>\varphi(1,0,2)=\Gamma_2</math>|| <math>\psi(\Omega^\Omega\times3)</math>
|-
| <math>(0)(1,1)(2,1)(3,1)(2,0)</math>|| <math>\varphi(1,0,\omega)=\Gamma_\omega</math>|| <math>\psi(\Omega^\Omega\times\omega)</math>
|-
| <math>(0)(1,1)(2,1)(3,1)(2,0)(3,1)(4,1)(5,1)</math>|| <math>\varphi(1,0,\varphi(1,0,0))=\Gamma_{\Gamma_0}</math>|| <math>\psi(\Omega^\Omega\times\psi(\Omega^\Omega))</math>
|-
| <math>(0)(1,1)(2,1)(3,1)(2,0)(3,1)(4,1)(5,1)(4,0)(5,1)(6,1)(7,1)</math>|| <math>\varphi(1,0,\varphi(1,0,\varphi(1,0,0)))=\Gamma_{\Gamma_{\Gamma_0}}</math>|| <math>\psi(\Omega^\Omega\times\psi(\Omega^\Omega\times\psi(\Omega^\Omega)))</math>
|-
| <math>(0)(1,1)(2,1)(3,1)(2,1)</math>|| <math>\varphi(1,1,0)</math>|| <math>\psi(\Omega^{\Omega+1})</math>
|-
| <math>(0)(1,1)(2,1)(3,1)(2,1)(2,1)</math>|| <math>\varphi(1,2,0)</math>|| <math>\psi(\Omega^{\Omega+2})</math>
|-
| <math>(0)(1,1)(2,1)(3,1)(2,1)(3,0)</math>|| <math>\varphi(1,\omega,0)</math>|| <math>\psi(\Omega^{\Omega+\omega})</math>
|-
| <math>(0)(1,1)(2,1)(3,1)(2,1)(3,0)(4,1)(5,1)(6,1)(5,1)(6,0)</math>|| <math>\varphi(1,\varphi(1,\omega,0),0)</math>|| <math>\psi(\Omega^{\Omega+\psi(\Omega^{\Omega+\omega})})</math>
|-
| <math>(0)(1,1)(2,1)(3,1)(2,1)(3,1)</math>|| <math>\psi(2,0,0)</math>|| <math>\psi(\Omega^{\Omega\times2})</math>
|-
| <math>(0)(1,1)(2,1)(3,1)(2,1)(3,1)(2,1)(3,1)</math>|| <math>\psi(3,0,0)</math>|| <math>\psi(\Omega^{\Omega\times3})</math>
|-
| <math>(0)(1,1)(2,1)(3,1)(3,0)</math>|| <math>\varphi(\omega,0,0)</math>|| <math>\psi(\Omega^{\Omega\times\omega})</math>
|-
| <math>(0)(1,1)(2,1)(3,1)(3,1)</math>|| <math>\varphi(1,0,0,0)</math>|| <math>\psi(\Omega^{\Omega^2})</math>
|-
| <math>(0)(1,1)(2,1)(3,1)(3,1)(3,1)</math>|| <math>\varphi(1,0,0,0,0)</math>|| <math>\psi(\Omega^{\Omega^3})</math>
|}
 
{| class="wikitable"
|-
! BMS !! MOCF
|-
| <math>(0)(1,1)(2,1)(3,1)(4,0)</math>|| <math>\psi(\Omega^{\Omega^\omega})</math>
|-
| <math>(0)(1,1)(2,1)(3,1)(4,0)(5,1)</math>|| <math>\psi(\Omega^{\Omega^{\psi(0)}})</math>
|-
| <math>(0)(1,1)(2,1)(3,1)(4,0)(5,1)(6,1)</math>|| <math>\psi(\Omega^{\Omega^{\psi(\Omega)}})</math>
|-
| <math>(0)(1,1)(2,1)(3,1)(4,0)(5,1)(6,1)(7,1)</math>|| <math>\psi(\Omega^{\Omega^{\psi(\Omega^\Omega)}})</math>
|-
| <math>(0)(1,1)(2,1)(3,1)(4,1)</math>|| <math>\psi(\Omega^{\Omega^\Omega})</math>
|-
| <math>(0)(1,1)(2,1)(3,1)(4,1)(5,1)</math>|| <math>\psi(\Omega^{\Omega^{\Omega^\Omega}})</math>
|-
| <math>(0)(1,1)(2,2)</math>|| <math>\psi(\psi_1(0))</math>
|-
| <math>(0)(1,1)(2,2)(1,1)</math>|| <math>\psi(\psi_1(0)+1)</math>
|-
| <math>(0)(1,1)(2,2)(1,1)(2,1)</math>|| <math>\psi(\psi_1(0)+\Omega)</math>
|-
| <math>(0)(1,1)(2,2)(1,1)(2,1)(3,1)</math>|| <math>\psi(\psi_1(0)+\Omega^\Omega)</math>
|-
| <math>(0)(1,1)(2,2)(1,1)(2,2)</math>|| <math>\psi(\psi_1(0)\times2)</math>
|-
| <math>(0)(1,1)(2,2)(2,0)</math>|| <math>\psi(\psi_1(0)\times\omega)</math>
|-
| <math>(0)(1,1)(2,2)(2,1)</math>|| <math>\psi(\psi_1(0)\times\Omega)</math>
|-
| <math>(0)(1,1)(2,2)(2,1)(3,0)</math>|| <math>\psi(\psi_1(0)\times\Omega^\omega)</math>
|-
| <math>(0)(1,1)(2,2)(2,1)(3,1)</math>|| <math>\psi(\psi_1(0)\times\Omega^\Omega)</math>
|-
| <math>(0)(1,1)(2,2)(2,1)(3,2)</math>|| <math>\psi(\psi_1(0)^2)</math>
|-
| <math>(0)(1,1)(2,2)(2,1)(3,2)(3,0)</math>|| <math>\psi(\psi_1(0)^\omega)</math>
|-
| <math>(0)(1,1)(2,2)(2,1)(3,2)(3,1)(4,2)</math>|| <math>\psi(\psi_1(0)^{\psi_1(0)})</math>
|-
| <math>(0)(1,1)(2,2)(2,2)</math>|| <math>\psi(\psi_1(1))</math>
|-
| <math>(0)(1,1)(2,2)(3,0)</math>|| <math>\psi(\psi_1(\omega))</math>
|-
| <math>(0)(1,1)(2,2)(3,1)(4,2)</math>|| <math>\psi(\psi_1(\psi_1(0)))</math>
|-
| <math>(0)(1,1)(2,2)(3,2)</math>|| <math>\psi(\Omega_2)</math>
|-
| <math>(0)(1,1)(2,2)(3,2)(1,1)</math>|| <math>\psi(\Omega_2+\Omega)</math>
|-
| <math>(0)(1,1)(2,2)(3,2)(1,1)(2,2)</math>|| <math>\psi(\Omega_2+\psi_1(0))</math>
|-
| <math>(0)(1,1)(2,2)(3,2)(1,1)(2,2)(3,1)(4,2)</math>|| <math>\psi(\Omega_2+\psi_1(\psi_1(0)))</math>
|-
| <math>(0)(1,1)(2,2)(3,2)(1,1)(2,2)(3,2)</math>|| <math>\psi(\Omega_2+\psi_1(\Omega_2))</math>
|-
| <math>(0)(1,1)(2,2)(3,2)(2,0)</math>|| <math>\psi(\Omega_2+\psi_1(\Omega_2)\times\omega)</math>
|-
| <math>(0)(1,1)(2,2)(3,2)(2,1)(3,2)(4,2)</math>|| <math>\psi(\Omega_2+\psi_1(\Omega_2)^2)</math>
|-
| <math>(0)(1,1)(2,2)(3,2)(2,1)(3,2)(4,2)(3,0)</math>|| <math>\psi(\Omega_2+\psi_1(\Omega_2)^\omega)</math>
|-
| <math>(0)(1,1)(2,2)(3,2)(2,1)(3,2)(4,2)(3,1)(4,2)(5,2)</math>|| <math>\psi(\Omega_2+\psi_1(\Omega_2)^{\psi_1(\Omega_2)})</math>
|-
| <math>(0)(1,1)(2,2)(3,2)(2,2)</math>|| <math>\psi(\Omega_2+\psi_1(\Omega_2+1))</math>
|-
| <math>(0)(1,1)(2,2)(3,2)(2,2)(3,0)</math>|| <math>\psi(\Omega_2+\psi_1(\Omega_2+\omega))</math>
|-
| <math>(0)(1,1)(2,2)(3,2)(2,2)(3,1)(4,2)(5,2)</math>|| <math>\psi(\Omega_2+\psi_1(\Omega_2+\psi_1(\Omega_2)))</math>
|-
| <math>(0)(1,1)(2,2)(3,2)(2,2)(3,1)(4,2)(5,2)(3,0)</math>|| <math>\psi(\Omega_2+\psi_1(\Omega_2+\psi_1(\Omega_2)\times\omega))</math>
|-
| <math>(0)(1,1)(2,2)(3,2)(2,2)(3,1)(4,2)(5,2)(4,0)</math>|| <math>\psi(\Omega_2+\psi_1(\Omega_2+\psi_1(\Omega_2)^\omega))</math>
|-
| <math>(0)(1,1)(2,2)(3,2)(2,2)(3,1)(4,2)(5,2)(4,1)(5,2)(6,2)</math>|| <math>\psi(\Omega_2+\psi_1(\Omega_2+\psi_1(\Omega_2)^{\psi_1(\Omega_2)}))</math>
|-
| <math>(0)(1,1)(2,2)(3,2)(2,2)(3,1)(4,2)(5,2)(4,2)</math>|| <math>\psi(\Omega_2+\psi_1(\Omega_2+\psi_1(\Omega_2+1)))</math>
|-
| <math>(0)(1,1)(2,2)(3,2)(2,2)(3,1)(4,2)(5,2)(4,2)(5,0)</math>|| <math>\psi(\Omega_2+\psi_1(\Omega_2+\psi_1(\Omega_2+\omega)))</math>
|-
| <math>(0)(1,1)(2,2)(3,2)(2,2)(3,1)(4,2)(5,2)(4,2)(5,0)(5,1)(6,2)(7,2)</math>|| <math>\psi(\Omega_2+\psi_1(\Omega_2+\psi_1(\Omega_2+\psi_1(\Omega_2))))</math>
|-
| <math>(0)(1,1)(2,2)(3,2)(2,2)(3,2)</math>|| <math>\psi(\Omega_2\times2)</math>
|-
| <math>(0)(1,1)(2,2)(3,2)(3,0)</math>|| <math>\psi(\Omega_2\times\omega)</math>
|-
| <math>(0)(1,1)(2,2)(3,2)(3,1)(4,2)(5,2)</math>|| <math>\psi(\Omega_2\times\psi_1(\Omega_2))</math>
|-
| <math>(0)(1,1)(2,2)(3,2)(3,2)</math>|| <math>\psi(\Omega_2^2)</math>
|-
| <math>(0)(1,1)(2,2)(3,2)(4,0)</math>|| <math>\psi(\Omega_2^\omega)</math>
|-
| <math>(0)(1,1)(2,2)(3,2)(4,2)</math>|| <math>\psi(\Omega_2^{\Omega_2})</math>
|-
| <math>(0)(1,1)(2,2)(3,3)</math>|| <math>\psi(\psi_2(0))</math>
|-
| <math>(0)(1,1)(2,2)(3,3)(4,3)</math>|| <math>\psi(\Omega_3)</math>
|-
| <math>(0)(1,1)(2,2)(3,3)(4,4)</math>|| <math>\psi(\psi_3(0))</math>
|-
| <math>(0)(1,1,1)=(0)(1,1)(2,2)(3,3)\cdots</math>|| <math>\psi(\Omega_\omega)</math>
|}
 
==== Part 3:三行 BMS (0)(1,1,1)~(0)(1,1,1)(2,1,0) ====
三行之后 BMS 的行为复杂度急剧上升,因此部分节点的分析可能不会较为详细。
 
{| class="wikitable"
|-
! BMS !! MOCF
|-
| <math>(0)(1,1,1)</math>|| <math>\psi(\Omega_\omega)</math>
|-
| <math>(0)(1,1,1)(1,1,0)</math>|| <math>\psi(\Omega_\omega+1)</math>
|-
| <math>(0)(1,1,1)(1,1,0)(2,0,0)</math>|| <math>\psi(\Omega_\omega+\omega)</math>
|-
| <math>(0)(1,1,1)(1,1,0)(2,1,0)</math>|| <math>\psi(\Omega_\omega+\Omega)</math>
|-
| <math>(0)(1,1,1)(1,1,0)(2,2,0)</math>|| <math>\psi(\Omega_\omega+\psi_1(0))</math>
|-
| <math>(0)(1,1,1)(1,1,0)(2,2,0)(2,2,0)</math>|| <math>\psi(\Omega_\omega+\psi_1(1))</math>
|-
| <math>(0)(1,1,1)(1,1,0)(2,2,0)(3,0,0)</math>|| <math>\psi(\Omega_\omega+\psi_1(\omega))</math>
|-
| <math>(0)(1,1,1)(1,1,0)(2,2,0)(3,1,0)(4,2,0)</math>|| <math>\psi(\Omega_\omega+\psi_1(\psi_1(0)))</math>
|-
| <math>(0)(1,1,1)(1,1,0)(2,2,0)(3,2,0)</math>|| <math>\psi(\Omega_\omega+\psi_1(\Omega_2))</math>
|-
| <math>(0)(1,1,1)(1,1,0)(2,2,0)(3,2,0)(2,0,0)</math>|| <math>\psi(\Omega_\omega+\psi_1(\Omega_2)\times\omega)</math>
|-
| <math>(0)(1,1,1)(1,1,0)(2,2,0)(3,2,0)(2,1,0)</math>|| <math>\psi(\Omega_\omega+\psi_1(\Omega_2)^\omega)</math>
|-
| <math>(0)(1,1,1)(1,1,0)(2,2,0)(3,2,0)(2,2,0)</math>|| <math>\psi(\Omega_\omega+\psi_1(\Omega_2+1))</math>
|-
| <math>(0)(1,1,1)(1,1,0)(2,2,0)(3,2,0)(2,2,0)(3,0,0)</math>|| <math>\psi(\Omega_\omega+\psi_1(\Omega_2+\omega))</math>
|-
| <math>(0)(1,1,1)(1,1,0)(2,2,0)(3,2,0)(2,2,0)(3,1,0)(4,2,0)</math>|| <math>\psi(\Omega_\omega+\psi_1(\Omega_2+\psi_1(0)))</math>
|-
| <math>(0)(1,1,1)(1,1,0)(2,2,0)(3,2,0)(2,2,0)(3,2,0)</math>|| <math>\psi(\Omega_\omega+\psi_1(\Omega_2\times2))</math>
|-
| <math>(0)(1,1,1)(1,1,0)(2,2,0)(3,2,0)(3,0,0)</math>|| <math>\psi(\Omega_\omega+\psi_1(\Omega_2\times\omega))</math>
|-
| <math>(0)(1,1,1)(1,1,0)(2,2,0)(3,2,0)(3,2,0)</math>|| <math>\psi(\Omega_\omega+\psi_1(\Omega_2^2))</math>
|-
| <math>(0)(1,1,1)(1,1,0)(2,2,0)(3,2,0)(4,2,0)</math>|| <math>\psi(\Omega_\omega+\psi_1(\Omega_2^{\Omega_2}))</math>
|-
| <math>(0)(1,1,1)(1,1,0)(2,2,0)(3,3,0)</math>|| <math>\psi(\Omega_\omega+\psi_1(\psi_2(0)))</math>
|-
| <math>(0)(1,1,1)(1,1,0)(2,2,0)(3,3,0)(4,4,0)</math>|| <math>\psi(\Omega_\omega+\psi_1(\psi_3(0)))</math>
|-
| <math>(0)(1,1,1)(1,1,0)(2,2,1)</math>|| <math>\psi(\Omega_\omega+\psi_1(\Omega_\omega))</math>
|-
| <math>(0)(1,1,1)(1,1,0)(2,2,1)(2,2,0)</math>|| <math>\psi(\Omega_\omega+\psi_1(\Omega_\omega+1))</math>
|-
| <math>(0)(1,1,1)(1,1,0)(2,2,1)(2,2,0)(3,0,0)</math>|| <math>\psi(\Omega_\omega+\psi_1(\Omega_\omega+\omega))</math>
|-
| <math>(0)(1,1,1)(1,1,0)(2,2,1)(2,2,0)(3,1,0)(4,2,0)</math>|| <math>\psi(\Omega_\omega+\psi_1(\Omega_\omega+\psi_1(0)))</math>
|-
| <math>(0)(1,1,1)(1,1,0)(2,2,1)(2,2,0)(3,1,0)(4,2,0)(5,3,0)</math>|| <math>\psi(\Omega_\omega+\psi_1(\Omega_\omega+\psi_1(\psi_2(0))))</math>
|-
| <math>(0)(1,1,1)(1,1,0)(2,2,1)(2,2,0)(3,1,0)(4,2,1)</math>|| <math>\psi(\Omega_\omega+\psi_1(\Omega_\omega+\psi_1(\Omega_\omega)))</math>
|-
| <math>(0)(1,1,1)(1,1,0)(2,2,1)(2,2,0)(3,2,0)</math>|| <math>\psi(\Omega_\omega+\Omega_2)</math>
|-
| <math>(0)(1,1,1)(1,1,0)(2,2,1)(2,2,0)(3,3,0)</math>|| <math>\psi(\Omega_\omega+\psi_2(0))</math>
|-
| <math>(0)(1,1,1)(1,1,0)(2,2,1)(2,2,0)(3,3,1)(3,3,0)(4,3,0)</math>|| <math>\psi(\Omega_\omega+\Omega_3)</math>
|-
| <math>(0)(1,1,1)(1,1,0)(2,2,1)(2,2,0)(3,3,1)(3,3,0)(4,4,0)</math>|| <math>\psi(\Omega_\omega+\psi_3(0))</math>
|-
| <math>(0)(1,1,1)(1,1,1)</math>|| <math>\psi(\Omega_\omega\times2)</math>
|-
| <math>(0)(1,1,1)(2,0,0)</math>|| <math>\psi(\Omega_\omega\times\omega)</math>
|-
| <math>(0)(1,1,1)(2,1,0)</math>|| <math>\psi(\Omega_\omega\times\Omega)</math>
|}
 
==== Part 4:(0)(1,1,1)(2,1,0)~(0)(1,1,1)(2,1,1) ====
这一部分涉及到[[提升效应]]
 
{| class="wikitable"
|-
! BMS !! MOCF
|-
| <math>(0)(1,1,1)(2,1,0)</math>|| <math>\psi(\Omega_\omega\times\Omega)</math>
|-
| <math>(0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)</math>|| <math>\psi(\Omega_\omega\times\Omega+\psi_1(\Omega_\omega))</math>
|-
| <math>(0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,0,0)</math>|| <math>\psi(\Omega_\omega\times\Omega+\psi_1(\Omega_\omega\times\omega))</math>
|-
| <math>(0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,1,0)</math>|| <math>\psi(\Omega_\omega\times\Omega+\psi_1(\Omega_\omega\times\Omega))</math>
|-
| <math>(0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,1,0)(2,2,0)</math>|| <math>\psi(\Omega_\omega\times\Omega+\psi_1(\Omega_\omega\times\Omega+1))</math>
|-
| <math>(0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,1,0)(2,2,0)(3,1,0)(4,2,0)</math>|| <math>\psi(\Omega_\omega\times\Omega+\psi_1(\Omega_\omega\times\Omega+\psi_1(0)))</math>
|-
| <math>(0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,1,0)(2,2,0)(3,1,0)(4,2,1)(5,1,0)</math>|| <math>\psi(\Omega_\omega\times\Omega+\psi_1(\Omega_\omega\times\Omega+\psi_1(\Omega_\omega\times\Omega)))</math>
|-
| <math>(0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,1,0)(2,2,0)(3,2,0)</math>|| <math>\psi(\Omega_\omega\times\Omega+\Omega_2)</math>
|-
| <math>(0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,1,0)(2,2,0)(3,3,0)</math>|| <math>\psi(\Omega_\omega\times\Omega+\psi_2(0))</math>
|-
| <math>(0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,1,0)(2,2,0)(3,3,1)(4,1,0)(3,3,0)(4,3,0)</math>|| <math>\psi(\Omega_\omega\times\Omega+\Omega_3)</math>
|-
| <math>(0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,1,0)(2,2,1)</math>|| <math>\psi(\Omega_\omega\times\Omega+\Omega_\omega)</math>
|-
| <math>(0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,1,0)(2,2,1)(1,1,0)(2,2,1)(3,1,0)</math>|| <math>\psi(\Omega_\omega\times\Omega+\Omega_\omega+\psi_1(\Omega_\omega\times\Omega))</math>
|-
| <math>(0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,1,0)(2,2,1)(1,1,0)(2,2,1)(3,1,0)(2,2,1)</math>|| <math>\psi(\Omega_\omega\times\Omega+\Omega_\omega+\psi_1(\Omega_\omega\times\Omega+\Omega_\omega))</math>
|-
| <math>(0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,1,0)(2,2,1)(2,0,0)</math>|| <math>\psi(\Omega_\omega\times\Omega+\Omega_\omega+\psi_1(\Omega_\omega\times\Omega+\Omega_\omega)\times\omega)</math>
|-
| <math>(0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,1,0)(2,2,1)(2,2,0)</math>|| <math>\psi(\Omega_\omega\times\Omega+\Omega_\omega+\psi_1(\Omega_\omega\times\Omega+\Omega_\omega+1))</math>
|-
| <math>(0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,1,0)(2,2,1)(2,2,0)(3,2,0)</math>|| <math>\psi(\Omega_\omega\times\Omega+\Omega_\omega+\Omega_2)</math>
|-
| <math>(0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,1,0)(2,2,1)(2,2,1)</math>|| <math>\psi(\Omega_\omega\times\Omega+\Omega_\omega\times2)</math>
|-
| <math>(0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,1,0)(2,2,1)(3,0,0)</math>|| <math>\psi(\Omega_\omega\times\Omega+\Omega_\omega\times\omega)</math>
|-
| <math>(0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,1,0)(2,2,1)(3,1,0)</math>|| <math>\psi(\Omega_\omega\times\Omega\times2)</math>
|-
| <math>(0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,1,0)(3,0,0)</math>|| <math>\psi(\Omega_\omega\times\Omega\times\omega)</math>
|-
| <math>(0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,1,0)(4,2,0)</math>|| <math>\psi(\Omega_\omega\times\psi_1(0))</math>
|-
| <math>(0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,1,0)(4,2,1)</math>|| <math>\psi(\Omega_\omega\times\psi_1(\Omega_\omega))</math>
|-
| <math>(0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,1,0)(4,2,1)(5,1,0)</math>|| <math>\psi(\Omega_\omega\times\psi_1(\Omega_\omega\times\Omega))</math>
|-
| <math>(0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,1,0)(4,2,1)(5,1,0)(4,2,1)</math>|| <math>\psi(\Omega_\omega\times\psi_1(\Omega_\omega\times\Omega+\Omega_\omega))</math>
|-
| <math>(0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,1,0)(4,2,1)(5,1,0)(4,2,1)(5,1,0)</math>|| <math>\psi(\Omega_\omega\times\psi_1(\Omega_\omega\times\Omega\times2)</math>
|-
| <math>(0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,1,0)(4,2,1)(5,1,0)(6,2,1)</math>|| <math>\psi(\Omega_\omega\times\psi_1(\Omega_\omega\times\psi_1(\Omega_\omega))</math>
|-
| <math>(0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,2,0)</math>|| <math>\psi(\Omega_\omega\times\Omega_2)</math>
|-
| <math>(0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,2,0)(2,2,0)(3,3,1)(4,2,0)(5,3,0)</math>|| <math>\psi(\Omega_\omega\times\psi_2(0))</math>
|-
| <math>(0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,2,0)(2,2,0)(3,3,1)(4,3,0)</math>|| <math>\psi(\Omega_\omega\times\Omega_3)</math>
|-
| <math>\color{red}{(0)(1,1,1)(2,1,0)(1,1,1)}</math>|| <math>\color{red}\psi(\Omega_\omega^2)</math>
|-
|<math>(0)(1,1,1)(2,1,0)(1,1,1)(1,1,0)</math>
|<math>\psi(\Omega_\omega^2+1)</math>
|-
|<math>(0)(1,1,1)(2,1,0)(1,1,1)(1,1,0)(2,2,1)</math>
|<math>\psi(\Omega_\omega^2+\psi_1(\Omega_\omega))</math>
|-
|<math>(0)(1,1,1)(2,1,0)(1,1,1)(1,1,0)(2,2,1)(3,1,0)</math>
|<math>\psi(\Omega_\omega^2+\psi_1(\Omega_\omega\times\Omega))</math>
|-
|<math>(0)(1,1,1)(2,1,0)(1,1,1)(1,1,0)(2,2,1)(3,1,0)(2,1,0)(3,2,1)(4,1,0)</math>
|<math>\psi(\Omega_\omega^2+\psi_1(\Omega_\omega\times\Omega+\psi_1(\Omega_\omega\times\Omega)))</math>
|-
|<math>(0)(1,1,1)(2,1,0)(1,1,1)(1,1,0)(2,2,1)(3,1,0)(2,2,0)(3,3,1)(4,1,0)</math>
|<math>\psi(\Omega_\omega^2+\psi_1(\Omega_\omega\times\Omega+\Omega_2))</math>
|-
|<math>(0)(1,1,1)(2,1,0)(1,1,1)(2,1,0)(1,1,1)</math>
|<math>\psi(\Omega_\omega^2\times2)</math>
|-
|<math>(0)(1,1,1)(2,1,0)(2,0,0)</math>
|<math>\psi(\Omega_\omega^2\times\omega)</math>
|-
|<math>(0)(1,1,1)(2,1,0)(2,1,0)</math>
|<math>\psi(\Omega_\omega^2\times\Omega)</math>
|-
|<math>(0)(1,1,1)(2,1,0)(2,1,0)(1,1,0)(2,2,1)</math>
|<math>\psi(\Omega_\omega^2\times\Omega+\psi_1(\Omega_\omega))</math>
|-
|<math>(0)(1,1,1)(2,1,0)(2,1,0)(1,1,0)(2,2,1)(3,1,0)(3,1,0)(2,2,1)</math>
|<math>\psi(\Omega_\omega^2\times\Omega+\Omega_\omega^2)</math>
|-
| <math>(0)(1,1,1)(2,1,0)(2,1,0)(1,1,0)(2,2,1)(3,2,0)(3,2,0)</math>|| <math>\psi(\Omega_\omega^2\times\Omega_2)</math>
|-
| <math>(0)(1,1,1)(2,1,0)(2,1,0)(1,1,0)(2,2,1)(3,2,0)(3,2,0)(2,2,0)(3,3,1)(4,3,0)(4,3,0)</math>|| <math>\psi(\Omega_\omega^2\times\Omega_3)</math>
|-
| <math>(0)(1,1,1)(2,1,0)(2,1,0)(1,1,1)</math>|| <math>\psi(\Omega_\omega^3)</math>
|-
| <math>(0)(1,1,1)(2,1,0)(2,1,0)(2,1,0)(1,1,1)</math>|| <math>\psi(\Omega_\omega^4)</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,0,0)</math>|| <math>\psi(\Omega_\omega^\omega)</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,1,0)</math>|| <math>\psi(\Omega_\omega^\Omega)</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,1,0)(1,1,1)</math>|| <math>\psi(\Omega_\omega^{\Omega_\omega})</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,1,0)(4,1,0)(1,1,1)</math>|| <math>\psi(\Omega_\omega^{\Omega_\omega^{\Omega_\omega}})</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,0)</math>|| <math>\psi(\psi_\omega(0))</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,0)(1,1,1)</math>|| <math>\psi(\psi_\omega(0)+\Omega_\omega)</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,0)(1,1,1)(2,1,0)(3,2,0)</math>|| <math>\psi(\psi_\omega(0)\times2)</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,0)(2,0,0)</math>|| <math>\psi(\psi_\omega(0)\times\omega)</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,0)(2,1,0)</math>|| <math>\psi(\psi_\omega(0)\times\Omega)</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,0)(2,1,0)(3,2,0)</math>|| <math>\psi(\psi_\omega(0)^2)</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,0)(3,0,0)</math>|| <math>\psi(\psi_\omega(0)^\omega)</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,0)(3,1,0)</math>|| <math>\psi(\psi_\omega(0)^\Omega)</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,0)(3,1,0)(4,2,0)</math>|| <math>\psi(\psi_\omega(0)^{\psi_\omega(0)})</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,0)(3,1,0)(4,2,0)(4,1,0)(5,2,0)</math>|| <math>\psi(\psi_\omega(0)^{\psi_\omega(0)^{\psi_\omega(0)}})</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,0)(3,2,0)</math>|| <math>\psi(\psi_\omega(1))</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,0)(3,2,0)(3,2,0)</math>|| <math>\psi(\psi_\omega(2))</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,0)(4,0,0)</math>|| <math>\psi(\psi_\omega(\omega))</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,0)(4,1,0)</math>|| <math>\psi(\psi_\omega(\Omega))</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,0)(4,1,0)(5,2,0)</math>|| <math>\psi(\psi_\omega(\psi_\omega(0)))</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,0)(4,2,0)</math>|| <math>\psi(\Omega_{\omega+1})</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,0)(4,2,0)(1,1,1)(2,1,1)(3,2,0)(4,2,0)</math>|| <math>\psi(\Omega_{\omega+1}+\psi_\omega(\Omega_{\omega+1}))</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,0)(4,2,0)(3,2,0)(4,2,0)</math>|| <math>\psi(\Omega_{\omega+1}\times2)</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,0)(4,2,0)(4,0,0)</math>|| <math>\psi(\Omega_{\omega+1}\times\omega)</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,0)(4,2,0)(4,1,0)</math>|| <math>\psi(\Omega_{\omega+1}\times\Omega)</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,0)(4,2,0)(4,2,0)</math>|| <math>\psi(\Omega_{\omega+1}^2)</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,0)(4,2,0)(5,0,0)</math>|| <math>\psi(\Omega_{\omega+1}^\omega)</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,0)(4,2,0)(5,1,0)</math>|| <math>\psi(\Omega_{\omega+1}^\Omega)</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,0)(4,2,0)(5,2,0)</math>|| <math>\psi(\Omega_{\omega+1}^{\Omega_{\omega+1}})</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,0)(4,3,0)</math>|| <math>\psi(\psi_{\omega+1}(0))</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,0)(4,3,0)(5,3,0)</math>|| <math>\psi(\Omega_{\omega+2})</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,0)(4,3,0)(5,4,0)</math>|| <math>\psi(\psi_{\omega+2}(0))</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,1)</math>|| <math>\psi(\Omega_{\omega\times2})</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,1)(1,1,1)</math>|| <math>\psi(\Omega_{\omega\times2}+\Omega_\omega)</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,1)(1,1,1)(2,1,0)(3,2,1)</math>|| <math>\psi(\Omega_{\omega\times2}+\psi_\omega(\Omega_{\omega\times2}))</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,1)(3,2,0)</math>|| <math>\psi(\Omega_{\omega\times2}+\psi_\omega(\Omega_{\omega\times2}+1))</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,1)(3,2,0)(4,1,0)(5,2,1)</math>|| <math>\psi(\Omega_{\omega\times2}+\psi_\omega(\Omega_{\omega\times2}+\psi_\omega(\Omega_{\omega\times2})))</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,1)(3,2,0)(4,2,0)</math>|| <math>\psi(\Omega_{\omega\times2}+\Omega_{\omega+1})</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,1)(3,2,0)(4,3,1)</math>|| <math>\psi(\Omega_{\omega\times2}+\psi_{\omega+1}(\Omega_{\omega\times2}))</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,1)(3,2,0)(4,3,1)(4,3,0)</math>|| <math>\psi(\Omega_{\omega\times2}+\psi_{\omega+1}(\Omega_{\omega\times2}+1))</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,1)(3,2,0)(4,3,1)(4,3,0)(5,2,0)</math>|| <math>\psi(\Omega_{\omega\times2}+\psi_{\omega+1}(\Omega_{\omega\times2}+\Omega_{\omega+1}))</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,1)(3,2,0)(4,3,1)(4,3,0)(5,2,0)</math>|| <math>\psi(\Omega_{\omega\times2}+\Omega_{\omega+2})</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,1)(3,2,1)</math>|| <math>\psi(\Omega_{\omega\times2}\times2)</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,1)(4,1,0)</math>|| <math>\psi(\Omega_{\omega\times2}\times\Omega)</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,1)(4,1,0)(1,1,1)</math>|| <math>\psi(\Omega_{\omega\times2}\times\Omega_\omega)</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,1)(4,1,0)(5,2,0)</math>|| <math>\psi(\Omega_{\omega\times2}\times\psi_\omega(0))</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,1)(4,1,0)(5,2,1)</math>|| <math>\psi(\Omega_{\omega\times2}\times\psi_\omega(\Omega_{\omega\times2}))</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,1)(4,2,0)</math>|| <math>\psi(\Omega_{\omega\times2}\times\Omega_{\omega+1})</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,1)(4,2,0)(3,2,0)(4,3,1)</math>|| <math>\psi(\Omega_{\omega\times2}\times\Omega_{\omega+1}+\psi_{\omega+1}(\Omega_{\omega\times2}))</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,1)(4,2,0)(3,2,0)(4,3,1)(5,2,0)(4,3,1)</math>|| <math>\psi(\Omega_{\omega\times2}\times\Omega_{\omega+1}+\Omega_{\omega\times2})</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,1)(4,2,0)(3,2,0)(4,3,1)(5,3,0)</math>|| <math>\psi(\Omega_{\omega\times2}\times\Omega_{\omega+2})</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,1)(4,2,0)(3,2,1)</math>|| <math>\psi(\Omega_{\omega\times2}^2)</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,1)(4,2,0)(4,2,0)(3,2,1)</math>|| <math>\psi(\Omega_{\omega\times2}^3)</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,1)(4,2,0)(5,0,0)</math>|| <math>\psi(\Omega_{\omega\times2}^\omega)</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,1)(4,2,0)(5,2,0)</math>|| <math>\psi(\Omega_{\omega\times2}^{\Omega_{\omega+1}})</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,1)(4,2,0)(5,2,0)(3,2,1)</math>|| <math>\psi(\Omega_{\omega\times2}^{\Omega_{\omega\times2}})</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,1)(4,2,0)(5,3,0)</math>|| <math>\psi(\psi_{\omega\times2}(0))</math>
|-
| <math>(0)(1,1,1)(2,1,0)(3,2,1)(4,2,0)(5,3,1)</math>|| <math>\psi(\Omega_{\omega\times3})</math>
|-
| <math>(0)(1,1,1)(2,1,1)</math>|| <math>\psi(\Omega_{\omega^2})</math>
|}


[[分类:分析]]
[[分类:分析]]

2025年8月24日 (日) 11:51的最新版本

本条目展示的分析来自最菜萌新

Part 1:0~BO

主词条:BMS分析Part1:0~BO

这个部分的BMS行为较为简单。

Part 2:BO~EBO

由于提升效应的出现,三行之后 BMS 的行为复杂度急剧上升。

主词条:BMS分析Part2:BO~EBO

Part 3:EBO~SSO

在这里,我们将正式引入投影序数

主词条:BMS分析Part3:EBO~SSO

Part4:SSO~pLRO

在我们的努力之下,一个“升级版”的BO浮出了水面。

主词条:BMS分析Part4:SSO~pLRO

Part5:pLRO~TSSO

在投影序数的助力下,我们抵达了三行BMS的终点,抵达了可怕与不可怕的分界点。

主词条:BMS分析Part5:pLRO~TSSO

Part6:TSSO~SHO

向上投影为我们揭示了BMS的ε0结构

主词条:BMS分析Part6BMS分析Part7