查看“︁序数表”︁的源代码

本条目列举出一些有名字的[[序数]]，它们大多在googology中具有重大意义

需要注意的是，它们的命名很多来自googology爱好者而非专业数学研究者。
== 序数表 ==
{| class="wikitable"
|+ 
|-
! 缩写 !! 英文全称 !! 常规表示方法(BOCF等) !! BMS/Y
|-
| FTO || First Transfinite Ordinal || <math>\omega</math>|| BMS(0)(1)
|-
| LAO || Linar Array Ordinal<ref>因为在googology一度经典的线性数阵的极限是它，因此得名</ref>|| <math>\omega^\omega</math>|| BMS(0)(1)(2)
|-
| [[SCO]]|| Small Cantor Ordinal || <math>\varphi(1,0)</math>|| BMS(0,0)(1,1)
|-
| [[CO]]|| Cantor Ordinal || <math>\varphi(2,0)</math>|| BMS(0,0)(1,1)(2,1)
|-
| [[HCO]]|| Hyper Cantor Ordinal || <math>\varphi(\omega,0)</math>|| BMS(0,0)(1,1)(2,1)(3,0)
|-
| [[FSO]]|| Feferman-Schutte Ordinal || φ(1,0,0) || BMS(0,0)(1,1)(2,1)(3,1)
|-
| [[SVO]]|| Small Veblen Ordinal || ψ(Ω^Ω^ω) || BMS(0,0)(1,1)(2,1)(3,1)(4,0)
|-
| [[LVO]]|| Large Veblen Ordinal || ψ(Ω^Ω^Ω) || BMS(0,0)(1,1)(2,1)(3,1)(4,1)
|-
| [[BHO]]|| Bachmann-Howard Ordinal || ψ(Ω_2) || BMS(0,0)(1,1)(2,2)
|-
| [[BO]]|| Buchholz's Ordinal || ψ(Ω_ω) || BMS(0,0,0)(1,1,1)
|-
| [[TFBO]]|| Takeuti-Feferman-Buchholz Ordinal || ψ(Ω_(ω+1)) || BMS(0,0,0)(1,1,1)(2,1,0)(3,2,0)
|-
| [[BIO]]|| Bird's Ordinal<ref>鸟之数阵第四版的极限是它，因此得名</ref>|| ψ(Ω_Ω) || BMS(0,0,0)(1,1,1)(2,1,1)(3,1,0)
|-
| [[EBO]]|| Extended Buchholz Ordinal || ψ(I) || BMS(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)
|-
| [[JO]]|| Jager's Ordinal || ψ(Ω_(I+1)) || BMS(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,0)
|-
| [[SIO]]|| Small Inaccessible Ordinal || ψ(I_ω) || BMS(0,0,0)(1,1,1)(2,1,1)(3,1,1)
|-
| [[MBO]]|| Mutiply Buchholz Ordinal || ψ(I(ω,0)) || BMS(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,0,0)
|-
| [[SRO]]|| Small Rathjen Ordinal || ψ(Ω_(M+1)) || BMS(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,0)
|-
| [[RO]]|| Rathjen's Ordinal || ψ(Ω_(K+1)) || BMS(0,0,0)(1,1,1)(2,1,1)(3,1,1)(4,1,0)(5,2,0)
|-
| [[SSO]]|| Small Stegert Ordinal || ψ(Π_ω) || BMS(0,0,0)(1,1,1)(2,2,0)
|-
| [[LSO]]|| Large Stegert Ordinal || ψ(λα.(α×2)-Π<sub>0</sub>) || BMS(0,0,0)(1,1,1)(2,2,0)(3,2,0)(4,1,0)(2,0,0)
|-
| [[BGO]]|| TSS 1st Back Gear Ordinal<ref>Bashicu对BGO的原定义是BMS(0,0,0)(1,1,1)(2,2,0)。BGO指(0,0,0)(1,1,1)(2,2,1)是中文googology社区的重命名</ref>|| ψ(Π<sub>1</sub>-λα.(Ω<sub>α+2</sub>)-Π<sub>1</sub>) || BMS(0,0,0)(1,1,1)(2,2,1)
|-
| [[SDO]]|| Small Dropping Ordinal || ψ(λα.(Ω<sub>α+ω</sub>)-Π<sub>0</sub>) || BMS(0,0,0)(1,1,1)(2,2,1)(3,0,0)
|-
| [[LDO]]|| Large Dropping Ordinal || ψ(λα.(OFP aft α)-Π<sub>0</sub>) || BMS(0,0,0)(1,1,1)(2,2,1)(3,2,0)
|-
| [[pLRO]]|| p.f.e.c. Large Rathjen Ordinal || ψ(ω-π-Π<sub>0</sub>) || BMS(0,0,0)(1,1,1)(2,2,2)
|-
| [[TSSO]]|| Trio Sequence System Ordinal || ψ(ω-projection) || BMS(0,0,0,0)(1,1,1,1)
|-
| [[QSSO]]|| Quardo Sequence System Ordinal || ψ(ψ<sub>H</sub>(H^H^ω))？ || BMS(0,0,0,0,0)(1,1,1,1,1)
|-
| [[SHO]]|| Small Hydra Ordinal || ψ(ψ<sub>H</sub>(H^^ω))？ || Y(1,3)
|-
| [[ΩSSO]]|| Ω Sequence System Ordinal || || Y(1,3,4,2,5,8,10)
|-
| [[GHO]]|| No-Go Hydra Ordinal || || Y(1,3,4,3)
|-
| [[SYO]]|| Small Yukito Ordinal || || ω-Y(1,4)
|-
| [[MHO]]|| Medium Hydra Ordinal || || ω-Y极限
|-
| [[CKO]]|| Church-Kleene Ordinal || ω<sub>1</sub><sup>CK</sup>||
|-
| FUO || First Uncountable Ordinal || ω<sub>1</sub> || 
|}