序数表：修订间差异
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创建页面，内容为“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 || ω || BMS(0)(1) |- | LAO || Linar Array Ordinal || ω^ω || BMS(0)(1)(2) |- | SCO || Small Cantor Ordinal || φ(1,0) || BMS…” |
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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 | 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。 | 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 == | == 序数表 == | ||
| 第9行： | 第10行： | ||
| FTO || First Transfinite Ordinal || ω || BMS(0)(1) | | FTO || First Transfinite Ordinal || ω || BMS(0)(1) | ||
|- | |- | ||
| LAO || Linar Array Ordinal || ω^ω || BMS(0)(1)(2) | | 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>|| ω^ω || BMS(0)(1)(2) | ||
|- | |- | ||
| SCO || Small Cantor Ordinal || φ(1,0) || BMS(0,0)(1,1) | | [[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) | | [[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) | | [[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) | | [[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) | | [[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) | | [[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) | | [[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) | | [[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) | | [[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) | | [[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) | | [[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) | | [[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) | | [[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) | | [[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) | | [[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) | | [[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> || | | FUO || First Uncountable Ordinal || ω<sub>1</sub> || | ||
|} | |} | ||
2025年7月2日 (三) 22:45的版本
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[1] | 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[2] | 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)-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[3] | 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 |