序数表
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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
| 缩写 | 英文全称 | 常规表示方法(BOCF等) | BMS/Y |
|---|---|---|---|
| FTO | First Transfinite Ordinal | ω | BMS(0)(1) |
| LAO | Linar Array Ordinal | ω^ω | BMS(0)(1)(2) |
| SCO | Small Cantor Ordinal | φ(1,0) | BMS(0,0)(1,1) |
| CO | Cantor Ordinal | φ(2,0) | BMS(0,0)(1,1)(2,1) |
| HCO | Hyper Cantor Ordinal | φ(ω,0) | 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 | 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) |
| DO | Duchhart's Ordinal | ψ(Ω_(κ+1)) | BMS(0,0,0)(1,1,1)(2,1,1)(3,1,1)(4,1,1)(5,1,0)(6,2,0) |
| 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)-Π0) | 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 | ψ(Π1-λα.(Ωα+2)-Π1) | BMS(0,0,0)(1,1,1)(2,2,1) |
| SDO | Small Dropping Ordinal | ψ(λα.(Ωα+ω)-Π0) | BMS(0,0,0)(1,1,1)(2,2,1)(3,0,0) |
| LDO | Large Dropping Ordinal | ψ(λα.(OFP aft α)-Π0) | BMS(0,0,0)(1,1,1)(2,2,1)(3,2,0) |
| pLRO | p.f.e.c. Large Rathjen Ordinal | ψ(ω-π-Π0) | 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(ψH(H^H^ω))？ | BMS(0,0,0,0,0)(1,1,1,1,1) |
| SHO | Small Hydra Ordinal | ψ(ψH(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 | ω1CK | |
| FUO | First Uncountable Ordinal | ω1 |