序数表：修订间差异

2025年9月7日 (日) 15:25的最新版本

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	$ω$	$B M S (0) (1)$
LAO	Linear Array Ordinal^[1]	$ω^{ω}$	$B M S (0) (1) (2)$
SCO	Small Cantor Ordinal	$φ (1, 0) = ε_{0} = ψ (Ω)$	$B M S (0, 0) (1, 1)$
CO	Cantor Ordinal	$φ (2, 0) = ζ_{0} = ψ (Ω^{2})$	$B M S (0, 0) (1, 1) (2, 1)$
LCO	Large Cantor Ordinal	$φ (3, 0) = η_{0} = ψ (Ω^{3})$	$B M S (0, 0) (1, 1) (2, 1) (2, 1)$
HCO	Hyper Cantor Ordinal	$φ (ω, 0) = ψ (Ω^{ω})$	$B M S (0, 0) (1, 1) (2, 1) (3, 0)$
FSO	Feferman-Schütte Ordinal	$φ (1, 0, 0) = Γ_{0} = ψ (Ω^{Ω})$	$B M S (0, 0) (1, 1) (2, 1) (3, 1)$
ACO	Ackermann Ordinal	$φ (1, 0, 0, 0) = ψ (Ω^{Ω^{2}})$	$B M S (0, 0) (1, 1) (2, 1) (3, 1) (3, 1)$
SVO	Small Veblen Ordinal	$ψ (Ω^{Ω^{ω}})$	$B M S (0, 0) (1, 1) (2, 1) (3, 1) (4, 0)$
LVO	Large Veblen Ordinal	$ψ (Ω^{Ω^{Ω}})$	$B M S (0, 0) (1, 1) (2, 1) (3, 1) (4, 1)$
BHO	Bachmann-Howard Ordinal	$ψ (Ω_{2})$	$B M S (0, 0) (1, 1) (2, 2)$
BO	Buchholz's Ordinal	$ψ (Ω_{ω})$	$B M S (0, 0, 0) (1, 1, 1)$
TFBO	Takeuti-Feferman-Buchholz Ordinal	$ψ (Ω_{ω + 1})$	$B M S (0, 0, 0) (1, 1, 1) (2, 1, 0) (3, 2, 0)$
BIO	Bird's Ordinal^[2]	$ψ (Ω_{Ω})$	$B M S (0, 0, 0) (1, 1, 1) (2, 1, 1) (3, 1, 0)$
EBO	Extended Buchholz Ordinal	$ψ (I)$	$B M S (0, 0, 0) (1, 1, 1) (2, 1, 1) (3, 1, 0) (2, 0, 0)$
JO	Jager's Ordinal	$ψ (Ω_{I + 1})$	$B M S (0, 0, 0) (1, 1, 1) (2, 1, 1) (3, 1, 0) (4, 2, 0)$
SIO	Small Inaccessible Ordinal	$ψ (I_{ω})$	$B M S (0, 0, 0) (1, 1, 1) (2, 1, 1) (3, 1, 1)$
MBO	Mutiply Buchholz Ordinal	$ψ (I (ω, 0)) = ψ (M^{ω})$	$B M S (0, 0, 0) (1, 1, 1) (2, 1, 1) (3, 1, 1) (3, 0, 0)$
TBO	Transfinitary Buchholz's Ordinal	$ψ (I (1, 0, 0)) = ψ (M^{M})$	$B M S (0, 0, 0) (1, 1, 1) (2, 1, 1) (3, 1, 1) (3, 1, 0) (2, 0, 0)$
SRO	Small Rathjen Ordinal	$ψ (ε_{M + 1})$	$B M S (0, 0, 0) (1, 1, 1) (2, 1, 1) (3, 1, 1) (3, 1, 0) (4, 2, 0)$
SMO	Small Mahlo Ordinal	$ψ (M_{ω})$	$B M S (0, 0, 0) (1, 1, 1) (2, 1, 1) (3, 1, 1) (3, 1, 1)$
SNO	Small 1-Mahlo (N) Ordinal	$ψ (N_{ω})$	$B M S (0, 0, 0) (1, 1, 1) (2, 1, 1) (3, 1, 1) (3, 1, 1) (3, 1, 1)$
RO	Rathjen's Ordinal	$ψ (ε_{K + 1})$	$B M S (0, 0, 0) (1, 1, 1) (2, 1, 1) (3, 1, 1) (4, 1, 0) (5, 2, 0)$
SKO	Small Weakly Compact (K) Ordinal	$ψ (K_{ω})$	$B M S (0, 0, 0) (1, 1, 1) (2, 1, 1) (3, 1, 1) (4, 1, 1)$
DO	Duchhart's Ordinal	$ψ (2 a f t 4)$	$B M S (0, 0, 0) (1, 1, 1) (2, 1, 1) (3, 1, 1) (4, 1, 1) (5, 1, 0) (6, 2, 0)$
SSO	Small Stegert Ordinal	$ψ (p s d . Π_{ω}) = ψ (a_{2})$	$B M S (0, 0, 0) (1, 1, 1) (2, 2, 0)$
LSO	Large Stegert Ordinal	$ψ (λ α . (α \times 2) - Π_{0}) = ψ (a_{2}^{a})$	$B M S (0, 0, 0) (1, 1, 1) (2, 2, 0) (3, 2, 0) (4, 1, 0) (2, 0, 0)$
APO	Admissible-parameter free effective cardinal Ordinal	$ψ (λ α . (Ω_{α + 1}) - Π_{1}) = ψ (a_{2}^{Ω_{a + 1}} + ψ_{a_{2}} (a_{2}^{Ω_{a + 1}}) \times ω)$	$B M S (0, 0, 0) (1, 1, 1) (2, 2, 0) (3, 2, 0) (4, 1, 1)$
BGO	TSS 1st Back Gear Ordinal (CN ggg)^[3]	$ψ (λ α . (Ω_{α + 2}) - Π_{1}) = ψ (Ω_{a_{2} + 1} + ψ_{a_{2}} (Ω_{a_{2} + 1}) \times ω)$	$B M S (0, 0, 0) (1, 1, 1) (2, 2, 1)$
SDO	Small Dropping Ordinal	$ψ (λ α . (Ω_{α + ω}) - Π_{0} = ψ (Ω_{a_{2} + 1} \times ω)$	$B M S (0, 0, 0) (1, 1, 1) (2, 2, 1) (3, 0, 0)$
LDO	Large Dropping Ordinal	$ψ (λ α . (ψ_{I_{α + 1}} (0)) - Π_{0}) = ψ (Ω_{a_{2} + 1} \times a_{2})$	$B M S (0, 0, 0) (1, 1, 1) (2, 2, 1) (3, 2, 0)$
DSO	Doubly +1 Stable Ordinal	$ψ (λ α . (λ β . β + 1 - Π_{0}) - Π_{0} = ψ (a_{3})$	$B M S (0, 0, 0) (1, 1, 1) (2, 2, 1) (3, 3, 0)$
TSO	Triply +1 Stable Ordinal	$ψ (λ α . (λ β . (λ γ . γ + 1 - Π_{0}) - Π_{0}) - Π_{0} = ψ (a_{4})$	$B M S (0, 0, 0) (1, 1, 1) (2, 2, 1) (3, 3, 1) (4, 4, 0)$
pfec LRO	pfec Large Rathjen Ordinal	$ψ (p f e c . ω - π - Π_{0}) = ψ (a_{ω})$	$B M S (0, 0, 0) (1, 1, 1) (2, 2, 2)$
SBO	Small Bashicu Ordinal	$ψ (p f e c . ω - π - Π_{0}) = ψ (a_{ω})$	$B M S (0, 0, 0) (1, 1, 1) (2, 2, 2)$
pfec M2O	pfec min Σ₂ Ordinal	$ψ (p f e c . \min (a ≺_{Σ_{1}} b ≺_{Σ_{2}} c))$	$B M S (0, 0, 0) (1, 1, 1) (2, 2, 2) (3, 2, 2) (4, 2, 2) (4, 2, 1)$ ？
LRO	Large Rathjen Ordinal	$F \cap ω_{1}^{CK}, θ = ω$	$⩽ B M S (0) (1, 1, 1, 1) ?$
TSSO / SSPO	Trio Sequence System Ordinal / Small Simple Projection Ordinal	$ψ (ω - proj.) = ψ (σ S \times ω) = ψ (H^{ω})$	$B M S (0) (1, 1, 1, 1)$
LSPO	Large Simple Projection Ordinal	$ψ (\min α is α - proj.) = ψ (σ S \times S)$	$B M S (0) (1, 1, 1, 1) (2, 1, 1, 1) (3, 1) (2)$
Q0.5BGO	QSS 0.5th Back Gear Ordinal	$ψ (ψ_{S} (σ S \times S \times ω + S_{2}))$	$B M S (0) (1, 1, 1, 1) (2, 2)$
Q1BGO	QSS 1st Back Gear Ordinal	$ψ (ψ_{S} (σ S \times S \times ω + S_{ω}))$	$B M S (0) (1, 1, 1, 1) (2, 2, 2)$
ESPO	Extend Simple Projection Ordinal	$ψ (ψ_{S} (σ S \times S \times ω^{2}))$	$B M S (0) (1, 1, 1, 1) (2, 2, 2, 1)$
BOBO	Big Omega Back Ordinal	$ψ ((ω, 0) - P) = ψ (ψ_{H} (H^{H ω}))$	$B M S (0) (1, 1, 1, 1) (2, 2, 2, 2)$
QSSO	Quardo Sequence System Ordinal	$ψ (ψ_{H} (H^{H^{ω}}))$	$B M S (0, 0, 0, 0, 0) (1, 1, 1, 1, 1)$
TCAO	Trio Comprehension Axiom Ordinal	$PTO ((Π_{3}^{1} - C A)_{0})$	$⩾ B M S (0) (1, 1, 1, 1, 1)$
QiSSO	Quinto Sequence System Ordinal	$ψ (ψ_{H} (H^{H^{H^{ω}}}))$	$B M S (0) (1, 1, 1, 1, 1, 1)$
SHO / BMO^[4]	Small Hydra Ordinal / Bashicu Matrix Ordinal	$ψ (ψ_{H} (ε_{H + 1})) ?$	$Y (1, 3) = \lim (B M S)$
βO	Beta Universe Ordinal	$P T O (Z_{2})$	$⩾ Y (1, 3)$
ΩSSO	Ω Sequence System Ordinal	$ψ (ψ_{H} (φ (Ω, H + 1))) ?$	$Y (1, 3, 4, 2, 5, 8, 10)$
LRPO	Large Right Projection Ordinal	$ψ (ψ_{H} (φ (H, 1))) ?$	$Y (1, 3, 4, 2, 5, 8, 10, 4, 9, 14, 17, 10)$
GHO	No-Go Hydra Ordinal^[5]	$ψ (ψ_{H} (ψ_{T} (T_{2} \times 2))) ?$	$Y (1, 3, 4, 3)$
DCO	Difference Catching Ordinal	$ψ (ψ_{H} (ψ_{T} (T_{2} \times ψ_{T} (T_{2}^{2})))) ?$	$Y (1, 3, 5)$
SYO	Small Yukito Ordinal	$ω M N (0) (,,, 1)$	$\lim (1 - Y) = ω - Y (1, 4)$
MHO / ωYO^[4]	Medium Hydra Ordinal / ω-Y sequence Ordinal	$ω 2 M N (0) (; 1)$	$\lim (ω - Y)$
CKO	Church-Kleene Ordinal	$ω_{1}^{C K}$
FUO	First Uncountable Ordinal	$ω_{1}$

已弃用序数表

缩写	英文全称	定义	大小	命名者
SMDO	Small Multidimensional Ordinal	$ω^{ω}$	$(0) (1) (2)$	318`4
SHO	Small Hydra Ordinal	$ε_{0} = ψ (Ω)$	$(0) (1, 1)$	FataliS1024
ESVO	Extended Small Veblen Ordinal	$ψ (Ω^{Ω^{Ω^{ω}}})$	$(0) (1, 1) (2, 1) (3, 1) (4, 1) (5)$
ELVO	Extended Large Veblen Ordinal	$ψ (Ω^{Ω^{Ω^{Ω}}})$	$(0) (1, 1) (2, 1) (3, 1) (4, 1) (5, 1)$
LDO(旧)	Large Dropping Ordinal	$ψ (λ α . (Ω_{α \times 2}) - Π_{0})$	$(0) (1, 1, 1) (2, 2, 1) (3, 1) (2)$
EDO	Extended Dropping Ordinal	$ψ (λ α . ψ_{I_{α + 1}} (I_{α + 1}) - Π_{0})$	$(0) (1, 1, 1) (2, 2, 1) (3, 2)$
SEIO	Small Eveog-Imagined Ordinal	$Σ_{1} adm.$
MEIO	Medium Eveog-Imagined Ordinal	$Σ_{2} adm.$
LEIO	Large Eveog-Imagined Ordinal	$Σ_{3} adm.$
SOSO	Second Order Stable Ordinal	$ψ (1 - o - Σ_{2} - stb.)$
EGO	Eveog's Ordinal	$ψ (ψ σ (σ_{ω}))$	$(0) (1, 1, 1, 1) (2, 2, 2, 1) (3, 2, 1) (4)$
MHO	Medium Hydra Ordinal	$\lim (B M S) = \lim (0 - Y)$	$Y (1, 3)$	FataliS1024
LHO	Large Hydra Ordinal	$\lim (ω - Y)$	$Ω - Y (1, 3, 12)$	FataliS1024
ZDO	Zeta Differenciating Ordinal	$FOS911 Θ (ζ_{0})$	$Ω - Y (1, 3, 12)$
WYO	Omega Y Ordinal	$\lim (Ω - Y)$	$Ω - Y (1, ω)$	318`4
EYO	Extended Y Ordinal	$bFOS Θ (BHO)$	$bFOS (0) (1) (ω) (ε_{0}) (BHO)$	318`4
UCO	Upgrade Catching Ordinal	$sFOS Θ (BHO)$	$bFOS Θ (BO)$	318`4
XYO	Extreme Y Ordinal	$bFOS Θ (BO)$	$bFOS (0) (1) (ω) (ε_{0}) (BO)$	318`4
DMO	Difference Matrix Ordinal	$sFOS Θ (BO)$	$bFOS Θ (SHO)$	318`4
GYO / 😰O	Grand Y-Sequence Ordinal / 😰 Ordinal	$\lim (X - Y)$	$sFOS (0) (1) (ω) (ε_{0}) (SHO)$	318`4
LDCO	Large Difference Catching Ordinal	$sFOS Θ (SYO)$	$b2-FOS Θ (ζ_{1})$	318`4
RHO	Remaining Hydra Ordinal	$\lim (sFOS)$	$b2-FOS Θ (φ (ω, 0))$	318`4
WFO	Omega Fundamental Ordinal	$\lim (Weak 2-FOS)$	$b2-FOS Θ (Γ_{0})$	318`4
TMDO	Tri-Multidimensional Ordinal	$s2-FOS Θ (φ (ω, 0))$	$ω 2 - RD$	318`4
ERHO	Extended Remaining hydra Ordinal	$\lim (b2-FOS)$	$ω 2 + 1 - RD$	318`4
LMDO	Large Multidimensional Ordinal	$\lim (ω - FOS)$	$ω^{2} - RD$	318`4
IFO	Infintesimal Function Ordinal	$\lim (IFS)$	$ε_{0} - RD$	318`4
WRO	Omega Remaining Ordinal	$\lim (ROS)$	$R Ω - Y$	318`4
SCLO	Small Code Lift Ordinal	$\sup (n - code)$
EHO	Huge Hydra Ordinal	$\lim (pfffz)$		夏夜星空
ROO	Remaining Omega Ordinal	$R_{ω} remaining$		318`4
UHO	Ultimate Hydra Ordinal	$\lim (RSAM)$		夏夜星空
IHO	Infinite Hydra Ordinal	$\lim (SAM)$		夏夜星空

本表取自 Worldly Sheet：

- （SCO/CO/LCO/HCO）谁起不重要，重要的是这是纪念康托尔的，如果没有他所有gggist今天(甚至永远)都走不到一起”
- 你们怎么把它弄成这样了，至少必要的（比如lim fffz/lim X-Y还是要的吧）
- fffz和X-Y公认理想之前搞这么多名字有什么用
- 不然MHO以上全都写成n-RD？- 不对 - 3184为什么要保留他造了那么多没用的序数缩写的黑历史？(bushi) - 不如还是加上毕竟fatalis的SHO/MHO/LHO都有了

DNAO

DNAO（Disgusting Nonsense Annoyance Ordinal）

定义：

(0)(1,1,1)(2,2,2)(3,3,3)(3,3,0)(4,4,1)(5,5,2)(6,6,2)(7,7,0)(8,8,1)(9,9,2)(10,9,2)(11,9,0)(12,10,1)(13,11,2)(13,11,2)(13,11,1)(14,12,2)(14,11,1)(15,12,2)(15,11,1)(16,12,0)(17,13,1)(18,14,2)(18,14,2)(18,14,1)(19,15,2)(19,14,1)(20,15,2)(20,14,1)(21,15,0)(22,16,1)(23,17,2)(23,17,2)(23,17,1)(24,18,2)(24,17,1)(25,18,2)(25,17,0)(26,18,1)(27,19,2)(27,19,2)(27,19,1)(28,20,2)(28,19,1)(29,20,2)(29,19,0)(30,20,1)(31,21,2)(31,21,2)(31,21,1)(32,22,2)(32,21,1)(33,22,2)(33,21,0)(34,22,1)(35,23,2)(35,23,2)(35,23,1)(36,24,2)(36,23,1)(37,24,2)(37,23,0)(38,24,1)(39,25,2)(40,25,2)(40,25,1)(41,26,2)(41,22,1)(42,23,2)(42,23,2)(42,23,1)(43,24,2)(43,23,1)(44,24,2)(44,23,0)(45,24,1)(46,25,2)(47,25,2)(47,25,1)(48,26,1)(49,27,0)(50,28,1)(51,29,2)(52,29,2)(52,29,1)(53,30,0)(54,31,1)(55,32,2)(56,32,2)(56,32,0)(57,33,1)(58,34,2)(59,34,2)(59,34,0)(60,35,1)(61,36,2)(62,36,2)(62,36,0)(63,37,1)(64,38,2)(65,38,2)(65,38,0)(66,39,1)(67,40,2)(68,40,2)(68,40,0)(69,41,1)(70,42,2)(71,42,2)(71,42,0)(72,43,1)(73,44,0)(74,45,1)(75,44,0)(76,45,1)(77,46,0)(78,47,0)(79,44,0)(80,45,1)(81,46,0)(82,47,0)(83,44,0)(84,45,1)(85,46,0)(86,47,0)(87,44,0)(88,45,1)(89,46,0)(90,47,0)(91,44,0)(92,45,1)(93,46,0)(94,47,0)(95,44,0)(96,45,1)(96,45,1)(96,45,1)(96,45,0)(97,46,0)(98,47,0)(99,48,0)(100,47,0)(101,48,0)(102,47,0)(103,48,0)(104,47,0)(105,48,0)(106,47,0)(107,48,0)(108,45,0)(109,46,0)(110,47,0)(111,47,0)(111,47,0)(111,47,0)(111,47,0)(111,47,0)(111,47,0)(111,46,0)(112,47,0)(113,47,0)(113,47,0)(113,47,0)(113,47,0)(113,47,0)(113,47,0)(113,46,0)(114,47,0)(115,46,0)(116,47,0)(117,46,0)(118,47,0)(119,46,0)(120,45,0)(121,46,0)(122,47,0)(123,47,0)(123,47,0)(123,47,0)(123,47,0)(123,47,0)(123,47,0)(123,46,0)(124,47,0)(125,47,0)(125,47,0)(125,47,0)(125,47,0)(125,47,0)(125,47,0)(125,46,0)(126,47,0)(127,46,0)(128,47,0)(129,46,0)(130,47,0)(131,46,0)(132,45,0)(133,46,0)(134,47,0)(135,47,0)(135,47,0)(135,47,0)(135,47,0)(135,47,0)(135,47,0)(135,46,0)(136,47,0)(137,47,0)(137,47,0)(137,47,0)(137,47,0)(137,47,0)(137,47,0)(137,46,0)(138,47,0)(139,46,0)(140,47,0)(141,46,0)(142,47,0)(143,46,0)(144,45,0)(145,46,0)(146,47,0)(147,47,0)(147,47,0)(147,47,0)(147,47,0)(147,47,0)(147,47,0)(147,46,0)(147,46,0)(147,46,0)(147,46,0)(147,46,0)(147,45,0)(148,46,0)(148,45,0)(149,46,0)(149,45,0)(150,46,0)(150,45,0)(151,45,0)(151,45,0)(150,45,0)(151,45,0)(150,45,0)(151,45,0)(148,45,0)(149,46,0)(149,45,0)(150,46,0)(150,45,0)(151,45,0)(151,45,0)(150,45,0)(151,45,0)(150,45,0)(151,45,0)(148,45,0)(149,46,0)(149,45,0)(150,46,0)(150,45,0)(151,45,0)(151,45,0)(150,45,0)(151,45,0)(150,45,0)(151,45,0)(148,45,0)(149,45,0)(149,45,0)(148,45,0)(149,45,0)(149,45,0)(148,45,0)(149,45,0)(147,45,0)(148,46,0)(148,45,0)(149,46,0)(149,45,0)(150,46,0)(150,45,0)(151,45,0)(151,45,0)(150,45,0)(151,45,0)(148,45,0)(149,46,0)(149,45,0)(150,45,0)(150,45,0)(149,45,0)(150,45,0)(149,45,0)(150,45,0)(149,45,0)(149,45,0)(149,45,0)(146,47,0)(147,47,0)(147,47,0)(147,47,0)(147,47,0)(147,47,0)(147,47,0)(147,46,0)(147,46,0)(147,46,0)(147,46,0)(147,45,0)(148,46,0)(149,47,0)(150,47,0)(150,47,0)(150,47,0)(150,47,0)(150,47,0)(150,47,0)(150,46,0)(150,46,0)(150,46,0)(150,46,0)(150,46,0)(150,45,0)(151,46,0)(151,45,0)(152,46,0)(152,45,0)(153,46,0)(153,45,0)(154,45,0)(154,45,0)(153,45,0)(154,45,0)(153,45,0)(154,45,0)(151,45,0)(152,46,0)(152,45,0)(153,46,0)(153,45,0)(154,45,0)(154,45,0)(153,45,0)(154,45,0)(153,45,0)(154,45,0)(151,45,0)(152,46,0)(152,45,0)(153,46,0)(153,45,0)(154,45,0)(154,45,0)(153,45,0)(154,45,0)(153,45,0)(154,45,0)(151,45,0)(152,45,0)(152,45,0)(151,45,0)(152,45,0)(152,45,0)(151,45,0)(152,45,0)(150,45,0)(151,46,0)(151,45,0)(152,46,0)(152,45,0)(153,46,0)(153,45,0)(154,45,0)(154,45,0)(153,45,0)(154,45,0)(151,45,0)(152,46,0)(152,45,0)(153,45,0)(153,45,0)(152,45,0)(153,45,0)(152,45,0)(153,45,0)(152,45,0)(152,45,0)(152,45,0)(149,47,0)(150,47,0)(150,47,0)(150,47,0)(150,47,0)(150,47,0)(150,47,0)(150,46,0)(150,46,0)(150,46,0)(150,46,0)(150,45,0)(151,46,0)(152,47,0)(152,47,0)(152,47,0)(151,45,0)(152,46,0)(153,47,0)(150,45,0)(151,46,0)(152,47,0)(152,47,0)(152,47,0)(151,45,0)(152,46,0)(153,47,0)(150,45,0)(151,46,0)(152,47,0)(150,45,0)(151,46,0)(152,47,0)(150,45,0)(151,45,0)(152,45,0)(152,45,0)(151,45,0)(152,45,0)(152,45,0)(150,45,0)(149,45,0)

脚注

↑ 因为在googology一度经典的线性数阵的极限是它，因此得名
↑ 鸟之数阵第四版的极限是它，因此得名
↑ 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
↑ ^4.0 ^4.1 SHO,MHO的名字均来自FataliS1024.但原定义的SHO指的是 $ε_{0}$ ,MHO指的是BMS极限。还有一个LHO指 $ω - Y$ 极限。但后来不知为何变成了现在的这个版本，而LHO成为了无定义的名字
↑ 原名Guo bu qu de Hydra Ordinal，但过于口语化和非正式。而这个序数本身确实是一个重要的序数。曹知秋将名字改成了现在的版本

[1] 因为在googology一度经典的线性数阵的极限是它，因此得名

[2] 鸟之数阵第四版的极限是它，因此得名

[3] 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

[:0-4] 4.0 ^4.1 SHO,MHO的名字均来自FataliS1024.但原定义的SHO指的是 $ε_{0}$ ,MHO指的是BMS极限。还有一个LHO指 $ω - Y$ 极限。但后来不知为何变成了现在的这个版本，而LHO成为了无定义的名字

[5] 原名Guo bu qu de Hydra Ordinal，但过于口语化和非正式。而这个序数本身确实是一个重要的序数。曹知秋将名字改成了现在的版本

[1]

[2]

[3]

[4]

[5]

@@ 第1行： / 第1行： @@
-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 ===
 {| class="wikitable"
-|+
 |-
-! 缩写 !! 英文全称 !! 常规表示方法(BOCF等) !! BMS/Y
+! 缩写 !! 英文全称 !! 常规表示方法（[[序数坍缩函数#BOCF|BOCF]] 等） !! [[BMS]] / [[Y序列|Y]]
+|-
+| [[FTO]]|| First Transfinite Ordinal || <math>\omega</math>|| <math>\mathrm{BMS}(0)(1)</math>
+|-
+| [[LAO]]|| Linear 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>|| <math>\mathrm{BMS}(0)(1)(2)</math>
+|-
+| [[SCO]]|| Small Cantor Ordinal || <math>\varphi(1,0)=\varepsilon_0=\psi(\Omega)</math>|| <math>\mathrm{BMS}(0,0)(1,1)</math>
+|-
+| [[CO]]|| Cantor Ordinal || <math>\varphi(2,0)=\zeta_0=\psi(\Omega^2)</math>|| <math>\mathrm{BMS}(0,0)(1,1)(2,1)</math>
+|-
+|[[LCO]]
+|Large Cantor Ordinal
+|<math>\varphi(3,0)=\eta_0=\psi(\Omega^3)</math>
+|<math>\mathrm{BMS}(0,0)(1,1)(2,1)(2,1)</math>
+|-
+| [[HCO]]|| Hyper Cantor Ordinal || <math>\varphi(\omega,0)=\psi(\Omega^\omega)</math>|| <math>\mathrm{BMS}(0,0)(1,1)(2,1)(3,0)</math>
+|-
+| [[FSO]]|| Feferman-Schütte Ordinal || <math>\varphi(1,0,0)=\Gamma_0=\psi(\Omega^\Omega)</math>|| <math>\mathrm{BMS}(0,0)(1,1)(2,1)(3,1)</math>
+|-
+|[[ACO]]
+|Ackermann Ordinal
+|<math>\varphi(1,0,0,0)=\psi(\Omega^{\Omega^2})</math>
+|<math>\mathrm{BMS}(0,0)(1,1)(2,1)(3,1)(3,1)</math>
+|-
+| [[SVO]]|| Small Veblen Ordinal || <math>\psi(\Omega^{\Omega^\omega})</math>|| <math>\mathrm{BMS}(0,0)(1,1)(2,1)(3,1)(4,0)</math>
+|-
+| [[LVO]]|| Large Veblen Ordinal || <math>\psi(\Omega^{\Omega^\Omega})</math>|| <math>\mathrm{BMS}(0,0)(1,1)(2,1)(3,1)(4,1)</math>
+|-
+| [[BHO]]|| Bachmann-Howard Ordinal || <math>\psi(\Omega_{2})</math>|| <math>\mathrm{BMS}(0,0)(1,1)(2,2)</math>
+|-
+| [[BO]]|| Buchholz's Ordinal || <math>\psi(\Omega_{\omega})</math>|| <math>\mathrm{BMS}(0,0,0)(1,1,1)</math>
+|-
+| [[TFBO]]|| Takeuti-Feferman-Buchholz Ordinal || <math>\psi(\Omega_{\omega+1})</math>|| <math>\mathrm{BMS}(0,0,0)(1,1,1)(2,1,0)(3,2,0)</math>
+|-
+| [[BIO]]|| Bird's Ordinal<ref>鸟之数阵第四版的极限是它，因此得名</ref>|| <math>\psi(\Omega_{\Omega})</math>|| <math>\mathrm{BMS}(0,0,0)(1,1,1)(2,1,1)(3,1,0)</math>
+|-
+| [[EBO]]|| Extended Buchholz Ordinal || <math>\psi(I)</math>|| <math>\mathrm{BMS}(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)</math>
+|-
+| [[JO]]|| Jager's Ordinal || <math>\psi(\Omega_{I+1})</math>|| <math>\mathrm{BMS}(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,0)</math>
+|-
+| [[SIO]]|| Small Inaccessible Ordinal || <math>\psi(I_{\omega})</math>|| <math>\mathrm{BMS}(0,0,0)(1,1,1)(2,1,1)(3,1,1)</math>
+|-
+| [[MBO]]|| Mutiply Buchholz Ordinal || <math>\psi(I(\omega,0))=\psi(M^\omega)</math>|| <math>\mathrm{BMS}(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,0,0)</math>
+|-
+|[[TBO]]
+|Transfinitary Buchholz's Ordinal
+|<math>\psi(I(1,0,0))=\psi(M^M)</math>
+|<math>\mathrm{BMS}(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,0,0)</math>
+|-
+| [[SRO]]|| Small Rathjen Ordinal || <math>\psi(\varepsilon_{M+1})</math>|| <math>\mathrm{BMS}(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,0)</math>
+|-
+| [[SMO]]|| Small Mahlo Ordinal || <math>\psi(M_\omega)</math>|| <math>\mathrm{BMS}(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)</math>
+|-
+|[[SNO]]
+|Small 1-Mahlo (N) Ordinal
+|<math>\psi(N_\omega)</math>
+|<math>\mathrm{BMS}(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(3,1,1)</math>
+|-
+| [[RO]]|| Rathjen's Ordinal || <math>\psi(\varepsilon_{K+1})</math>|| <math>\mathrm{BMS}(0,0,0)(1,1,1)(2,1,1)(3,1,1)(4,1,0)(5,2,0)</math>
+|-
+|[[SKO]]
+|Small Weakly Compact (K) Ordinal
+|<math>\psi(K_\omega)</math>
+|<math>\mathrm{BMS}(0,0,0)(1,1,1)(2,1,1)(3,1,1)(4,1,1)</math>
+|-
+|[[DO]]
+|Duchhart's Ordinal
+|<math>\psi(2 \ \rm{aft} \ 4)</math>
+|<math>\mathrm{BMS}(0,0,0)(1,1,1)(2,1,1)(3,1,1)(4,1,1)(5,1,0)(6,2,0)</math>
+|-
+| [[SSO]]|| Small Stegert Ordinal || <math>\psi(psd.\Pi_{\omega})=\psi(a_2)</math>|| <math>\mathrm{BMS}(0,0,0)(1,1,1)(2,2,0)</math>
+|-
+| [[LSO]]|| Large Stegert Ordinal || <math>\psi(\lambda\alpha.(\alpha\times 2)-\Pi_{0})=\psi(a_2^a)</math>|| <math>\mathrm{BMS}(0,0,0)(1,1,1)(2,2,0)(3,2,0)(4,1,0)(2,0,0)</math>
+|-
+|[[APO]]
+|Admissible-parameter free effective cardinal Ordinal
+|<math>\psi(\lambda\alpha.(\Omega_{\alpha+1})-\Pi_1)=\psi(a_2^{\Omega_{a+1}}+\psi_{a_2}(a_2^{\Omega_{a+1}})\times\omega)</math>
+|<math>\mathrm{BMS}(0,0,0)(1,1,1)(2,2,0)(3,2,0)(4,1,1)</math>
+|-
+| [[BGO]]|| TSS 1st Back Gear Ordinal (CN ggg)<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>|| <math>\psi(\lambda\alpha.(\Omega_{\alpha+2})-\Pi_{1})=\psi(\Omega_{a_2+1}+\psi_{a_2}(\Omega_{a_2+1})\times\omega)</math>|| <math>\mathrm{BMS}(0,0,0)(1,1,1)(2,2,1)</math>
+|-
+| [[SDO]]|| Small Dropping Ordinal || <math>\psi(\lambda\alpha.(\Omega_{\alpha+\omega})-\Pi_{0}=\psi(\Omega_{a_2+1}\times\omega)</math>|| <math>\mathrm{BMS}(0,0,0)(1,1,1)(2,2,1)(3,0,0)</math>
+|-
+| [[LDO]]|| Large Dropping Ordinal || <math>\psi(\lambda\alpha.(\psi_{I_{\alpha+1}}(0))-\Pi_{0})=\psi(\Omega_{a_2+1}\times a_2)</math>|| <math>\mathrm{BMS}(0,0,0)(1,1,1)(2,2,1)(3,2,0)</math>
+|-
+|[[DSO]]
+|Doubly +1 Stable Ordinal
+|<math>\psi(\lambda\alpha.(\lambda\beta.\beta+1-\Pi_0)-\Pi_0=\psi(a_3) </math>
+|<math>\mathrm{BMS}(0,0,0)(1,1,1)(2,2,1)(3,3,0)</math>
+|-
+|[[TSO]]
+|Triply +1 Stable Ordinal
+|<math>\psi(\lambda\alpha.(\lambda\beta.(\lambda\gamma.\gamma+1-\Pi_0)-\Pi_0)-\Pi_0=\psi(a_4) </math>
+|<math>\mathrm{BMS}(0,0,0)(1,1,1)(2,2,1)(3,3,1)(4,4,0)</math>
+|-
+| [[LRO|pfec LRO]]|| pfec Large Rathjen Ordinal || <math>\psi(pfec.\omega-\pi-\Pi_{0})=\psi(a_\omega)</math>|| <math>\mathrm{BMS}(0,0,0)(1,1,1)(2,2,2)</math>
+|-
+|[[LRO|SBO]]
+|Small Bashicu Ordinal
+| <math>\psi(pfec.\omega-\pi-\Pi_{0})=\psi(a_\omega) </math>
+|<math>\mathrm{BMS}(0,0,0)(1,1,1)(2,2,2)</math>
+|-
+|[[方括号稳定|pfec M2O]]
+|pfec min Σ<sub>2</sub> Ordinal
+|<math>\psi(pfec.\min(a\prec_{\Sigma_1}b\prec_{\Sigma_2}c)) </math>
+|<math>\mathrm{BMS}(0,0,0)(1,1,1)(2,2,2)(3,2,2)(4,2,2)(4,2,1)</math>？
+|-
+|[[LRO]]
+|Large Rathjen Ordinal
+|<math>F\cap\omega_1^\text{CK},\theta=\omega </math>
+|<math>\leqslant\mathrm{BMS}(0)(1,1,1,1)?</math>
+|-
+|[[TSSO]] / SSPO
+|Trio Sequence System Ordinal / Small Simple Projection Ordinal
+|<math>\psi(\omega-\text{proj.})=\psi(\sigma S\times \omega)=\psi(H^\omega)</math>
+|<math>\mathrm{BMS}(0)(1,1,1,1)</math>
+|-
+|[[LSPO]]
+|Large Simple Projection Ordinal
+|<math>\psi(\min\ \alpha\text{ is }\alpha-\text{proj.})=\psi(\sigma S\times S) </math>
+|<math>\mathrm{BMS}(0)(1,1,1,1)(2,1,1,1)(3,1)(2)</math>
+|-
+|[[Q0.5BGO]]
+|QSS 0.5th Back Gear Ordinal
+|<math>\psi(\psi_S(\sigma S\times S\times \omega+S_2)) </math>
+|<math>\rm{BMS}(0)(1,1,1,1)(2,2)</math>
+|-
+|[[Q1BGO]]
+|QSS 1st Back Gear Ordinal
+| <math>\psi(\psi_S(\sigma S\times S\times \omega+S_\omega)) </math>
+|<math>\mathrm{BMS}(0)(1,1,1,1)(2,2,2)</math>
+|-
+|[[ESPO]]
+|Extend Simple Projection Ordinal
+| <math>\psi(\psi_S(\sigma S\times S\times \omega^2)) </math>
+|<math>\mathrm{BMS}(0)(1,1,1,1)(2,2,2,1)</math>
+|-
+|[[BOBO]]
+|Big Omega Back Ordinal
+| <math>\psi((\omega,0)-P)=\psi(\psi_{H}(H^{H\omega})) </math>
+|<math>\mathrm{BMS}(0)(1,1,1,1)(2,2,2,2)</math>
+|-
+| [[QSSO]]|| Quardo Sequence System Ordinal || <math>\psi(\psi_{H}(H^{H^{\omega}}))</math>|| <math>\mathrm{BMS}(0,0,0,0,0)(1,1,1,1,1)</math>
+|-
+|[[QSSO|TCAO]]
+|Trio Comprehension Axiom Ordinal
+|<math>\text{PTO}((\Pi_3^1-CA)_0) </math>
+|<math>\geqslant\mathrm{BMS}(0)(1,1,1,1,1)</math>
+|-
+|QiSSO
+|Quinto Sequence System Ordinal
+| <math>\psi(\psi_{H}(H^{H^{H^{\omega}}}))</math>
+|<math>\mathrm{BMS}(0)(1,1,1,1,1,1)</math>
+|-
+| [[SHO]] / BMO<ref name=":0">SHO,MHO的名字均来自FataliS1024.但原定义的SHO指的是<math>\varepsilon_0</math>,MHO指的是BMS极限。还有一个LHO指<math>\omega -Y</math>极限。但后来不知为何变成了现在的这个版本，而LHO成为了无定义的名字</ref>|| Small Hydra Ordinal / Bashicu Matrix Ordinal || <math>\psi(\psi_{H}(\varepsilon_{H+1}))?</math>|| <math>Y(1,3)=\lim(\rm BMS)</math>
+|-
+|βO
+|Beta Universe Ordinal
+|<math>\rm PTO(Z_2)</math>
+|<math>\geqslant Y(1,3)</math>
+|-
+| [[ΩSSO]]|| Ω Sequence System Ordinal || <math>\psi(\psi_H(\varphi(\Omega,H+1)))?</math>|| <math>Y(1,3,4,2,5,8,10)</math>
+|-
+|[[LRPO]]
+|Large Right Projection Ordinal
+|<math>\psi(\psi_{H}(\varphi(H,1)))?</math>
+|<math>Y(1,3,4,2,5,8,10,4,9,14,17,10)</math>
+|-
+| [[GHO]]|| No-Go Hydra Ordinal<ref>原名Guo bu qu de Hydra Ordinal，但过于口语化和非正式。而这个序数本身确实是一个重要的序数。曹知秋将名字改成了现在的版本</ref>|| <math>\psi(\psi_H(\psi_T(T_2\times 2)))?</math>|| <math>Y(1,3,4,3)</math>
+|-
+|[[DCO]]
+|Difference Catching Ordinal
+|<math>\psi(\psi_H(\psi_T(T_2\times\psi_T(T_2^2))))?</math>
+|<math>Y(1,3,5)</math>
+|-
+| [[SYO]]|| Small Yukito Ordinal || <math>\omega \rm{ MN}(0)(,,,1)</math>|| <math>\lim(1-Y)=\omega-Y(1,4)</math>
+|-
+| [[MHO]] / ωYO<ref name=":0" />|| Medium Hydra Ordinal / ω-Y sequence Ordinal || <math>\omega \rm{2MN}(0)(;1)</math>|| <math>\lim(\omega-Y)</math>
+|-
+| [[CKO]]|| Church-Kleene Ordinal || <math>\omega_{1}^{\rm CK}</math>
 |-
-| FTO || First Transfinite Ordinal || <math>\omega</math>|| <math>BMS(0)(1)</math>
+| [[FUO]]|| First Uncountable Ordinal || <math>\omega_{1}</math>||
+|}
+=== 已弃用序数表 ===
+{| class="wikitable"
+!缩写
+!英文全称
+!定义
+!大小
+!命名者
 |-
-| 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>|| <math>BMS(0)(1)(2)</math>
+|SMDO
+|Small Multidimensional Ordinal
+|<math>\omega^\omega</math>
+|<math>(0)(1)(2)</math>
+|318`4
 |-
-| [[SCO]]|| Small Cantor Ordinal || <math>\varphi(1,0)=\varepsilon_0=\psi(\Omega)</math>|| <math>BMS(0,0)(1,1)</math>
+|SHO
+|Small Hydra Ordinal
+|<math>\varepsilon_0=\psi(\Omega)</math>
+|<math>(0)(1,1)</math>
+|FataliS1024
 |-
-| [[CO]]|| Cantor Ordinal || <math>\varphi(2,0)=\zeta_0=\psi(\Omega^2)</math>|| <math>BMS(0,0)(1,1)(2,1)</math>
+|ESVO
+|Extended Small Veblen Ordinal
+|<math>\psi\left(\Omega^{\Omega^{\Omega^{\omega}}}\right)</math>
+|<math>(0)(1,1)(2,1)(3,1)(4,1)(5)</math>
+|
 |-
-| [[HCO]]|| Hyper Cantor Ordinal || <math>\varphi(\omega,0)=\psi(\Omega^\omega)</math>|| <math>BMS(0,0)(1,1)(2,1)(3,0)</math>
+|ELVO
+|Extended Large Veblen Ordinal
+|<math>\psi\left(\Omega^{\Omega^{\Omega^{\Omega}}}\right)</math>
+|<math>(0)(1,1)(2,1)(3,1)(4,1)(5,1)</math>
+|
 |-
-| [[FSO]]|| Feferman-Schutte Ordinal || <math>\varphi(1,0,0)=\Gamma_0=\psi(\Omega^\Omega)</math>|| <math>BMS(0,0)(1,1)(2,1)(3,1)</math>
+|LDO(旧)
+|Large Dropping Ordinal
+|<math>\psi(\lambda\alpha.(\Omega_{\alpha\times 2})-\Pi_{0})</math>
+|<math>(0)(1,1,1)(2,2,1)(3,1)(2)</math>
+|
 |-
-| [[SVO]]|| Small Veblen Ordinal || <math>\psi(\Omega^{\Omega^{\omega}})</math>|| <math>BMS(0,0)(1,1)(2,1)(3,1)(4,0)</math>
+|EDO
+|Extended Dropping Ordinal
+|<math>\psi(\lambda\alpha.\psi_{I_{\alpha+1}}(I_{\alpha+1})-\Pi_0)</math>
+|<math>(0)(1,1,1)(2,2,1)(3,2)</math>
+|
 |-
-| [[LVO]]|| Large Veblen Ordinal || <math>\psi(\Omega^{\Omega^{\Omega}})</math>|| <math>BMS(0,0)(1,1)(2,1)(3,1)(4,1)</math>
+|SEIO
+|Small Eveog-Imagined Ordinal
+|<math>\Sigma_1\text{ adm.}</math>
+|
+|
 |-
-| [[BHO]]|| Bachmann-Howard Ordinal || <math>\psi(\Omega_{2})</math>|| <math>BMS(0,0)(1,1)(2,2)</math>
+|MEIO
+|Medium Eveog-Imagined Ordinal
+|<math>\Sigma_2\text{ adm.}</math>
+|
+|
 |-
-| [[BO]]|| Buchholz's Ordinal || <math>\psi(\Omega_{\omega})</math>|| <math>BMS(0,0,0)(1,1,1)</math>
+|LEIO
+|Large Eveog-Imagined Ordinal
+|<math>\Sigma_3\text{ adm.}</math>
+|
+|
 |-
-| [[TFBO]]|| Takeuti-Feferman-Buchholz Ordinal || <math>\psi(\Omega_{\omega+1})</math>|| <math>BMS(0,0,0)(1,1,1)(2,1,0)(3,2,0)</math>
+|SOSO
+|Second Order Stable Ordinal
+|<math>\psi(1-o-\Sigma_2-\text{stb.})</math>
+|
+|
 |-
-| [[BIO]]|| Bird's Ordinal<ref>鸟之数阵第四版的极限是它，因此得名</ref>|| <math>\psi(\Omega_{\Omega})</math>|| <math>BMS(0,0,0)(1,1,1)(2,1,1)(3,1,0)</math>
+|EGO
+|Eveog's Ordinal
+|<math>\psi(\psi\sigma(\sigma_\omega))</math>
+|<math>(0)(1,1,1,1)(2,2,2,1)(3,2,1)(4)</math>
+|
 |-
-| [[EBO]]|| Extended Buchholz Ordinal || <math>\psi(I)</math>|| <math>BMS(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)</math>
+|MHO
+|Medium Hydra Ordinal
+|<math>\lim({\rm BMS})=\lim(0-Y)</math>
+|<math>Y(1,3)</math>
+|FataliS1024
 |-
-| [[JO]]|| Jager's Ordinal || <math>\psi(\Omega_{I+1})</math>|| <math>BMS(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,0)</math>
+|LHO
+|Large Hydra Ordinal
+|<math>\lim(\omega-Y)</math>
+|<math>\Omega-Y(1,3,12)</math>
+|FataliS1024
 |-
-| [[SIO]]|| Small Inaccessible Ordinal || <math>\psi(I_{\omega})</math>|| <math>BMS(0,0,0)(1,1,1)(2,1,1)(3,1,1)</math>
+|ZDO
+|Zeta Differenciating Ordinal
+|<math>\text{FOS911 }\Theta(\zeta_0)</math>
+|<math>\Omega-Y(1,3,12)</math>
+|
 |-
-| [[MBO]]|| Mutiply Buchholz Ordinal || <math>\psi(I(\omega,0))=\psi(M^\omega)</math>|| <math>BMS(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,0,0)</math>
+|WYO
+|Omega Y Ordinal
+|<math>\lim(\Omega-Y)</math>
+|<math>\Omega-Y(1,\omega)</math>
+|318`4
 |-
-| [[SRO]]|| Small Rathjen Ordinal || <math>\psi(\varepsilon_{M+1})</math>|| <math>BMS(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,0)</math>
+|EYO
+|Extended Y Ordinal
+|<math>\text{bFOS }\Theta(\text{BHO})</math>
+|<math>\text{bFOS }(0)(1)(\omega)(\varepsilon_0)(\text{BHO})</math>
+|318`4
 |-
-| [[SMO]]|| Small Mahlo Ordinal || <math>\psi(M_\omega)</math>|| <math>BMS(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)</math>
+|UCO
+|Upgrade Catching Ordinal
+|<math>\text{sFOS }\Theta(\text{BHO})</math>
+|<math>\text{bFOS }\Theta(\text{BO})</math>
+|318`4
 |-
-| [[RO]]|| Rathjen's Ordinal || <math>\psi(\varepsilon_{K+1})</math>|| <math>BMS(0,0,0)(1,1,1)(2,1,1)(3,1,1)(4,1,0)(5,2,0)</math>
+|XYO
+|Extreme Y Ordinal
+|<math>\text{bFOS }\Theta(\text{BO})</math>
+|<math>\text{bFOS }(0)(1)(\omega)(\varepsilon_0)(\text{BO})</math>
+|318`4
 |-
-| [[SSO]]|| Small Stegert Ordinal || <math>\psi(\Pi_{\omega})=\psi(a_2)</math>|| <math>BMS(0,0,0)(1,1,1)(2,2,0)</math>
+|DMO
+|Difference Matrix Ordinal
+|<math>\text{sFOS }\Theta(\text{BO})</math>
+|<math>\text{bFOS }\Theta(\text{SHO})</math>
+|318`4
 |-
-| [[LSO]]|| Large Stegert Ordinal || <math>\psi(\lambda\alpha.(\alpha\times 2)-\Pi_{0})=\psi(a_2^a)</math>|| <math>BMS(0,0,0)(1,1,1)(2,2,0)(3,2,0)(4,1,0)(2,0,0)</math>
+|GYO / 😰O
+|Grand Y-Sequence Ordinal / 😰 Ordinal
+|<math>\lim(X-Y)</math>
+|<math>\text{sFOS }(0)(1)(\omega)(\varepsilon_0)(\text{SHO})</math>
+|318`4
 |-
-| [[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>|| <math>\psi(\Pi_{1}-\lambda\alpha.(\Omega_{\alpha+2})-\Pi_{1})</math>|| <math>BMS(0,0,0)(1,1,1)(2,2,1)</math>
+|LDCO
+|Large Difference Catching Ordinal
+|<math>\text{sFOS }\Theta(\text{SYO})</math>
+|<math>\text{b2-FOS }\Theta(\zeta_1)</math>
+|318`4
 |-
-| [[SDO]]|| Small Dropping Ordinal || <math>\psi(\lambda\alpha.(\Omega_{\alpha+\omega})-\Pi_{0})</math>|| <math>BMS(0,0,0)(1,1,1)(2,2,1)(3,0,0)</math>
+|RHO
+|Remaining Hydra Ordinal
+|<math>\lim(\text{sFOS})</math>
+|<math>\text{b2-FOS }\Theta(\varphi(\omega,0))</math>
+|318`4
 |-
-| [[LDO]]|| Large Dropping Ordinal || <math>\psi(\lambda\alpha.(\mathrm{OFP}\ \mathrm{aft}\ \alpha)-\Pi_{0})</math>|| <math>BMS(0,0,0)(1,1,1)(2,2,1)(3,2,0)</math>
+|WFO
+|Omega Fundamental Ordinal
+|<math>\lim(\text{Weak 2-FOS})</math>
+|<math>\text{b2-FOS }\Theta(\Gamma_0)</math>
+|318`4
 |-
-| [[pLRO]]|| p.f.e.c. Large Rathjen Ordinal || <math>\psi(\omega-\pi-\Pi_{0})=\psi(a_\omega) </math>|| <math>BMS(0,0,0)(1,1,1)(2,2,2)</math>
+|TMDO
+|Tri-Multidimensional Ordinal
+|<math>\text{s2-FOS }\Theta(\varphi(\omega,0))</math>
+|<math>\omega2-\text{RD}</math>
+|318`4
 |-
-| [[TSSO]]|| Trio Sequence System Ordinal || <math>\psi(\omega-projection)=\psi(\sigma S\times S)=\psi(H^\omega)</math>|| <math>BMS(0,0,0,0)(1,1,1,1)</math>
+|ERHO
+|Extended Remaining hydra Ordinal
+|<math>\lim(\text{b2-FOS})</math>
+|<math>\omega2+1-\text{RD}</math>
+|318`4
 |-
-| [[QSSO]]|| Quardo Sequence System Ordinal || <math>\psi(\psi_{H}(H^{H^{\omega}}))?</math>|| <math>BMS(0,0,0,0,0)(1,1,1,1,1)</math>
+|LMDO
+|Large Multidimensional Ordinal
+|<math>\lim(\omega-\text{FOS})</math>
+|<math>\omega^2-\text{RD}</math>
+|318`4
 |-
-| SHO/BMO|| Small Hydra Ordinal || <math>\psi(\psi_{H}(\varepsilon_{H+1}))?</math>|| <math>Y(1,3)=BMS\text{极限}</math>
+|IFO
+|Infintesimal Function Ordinal
+|<math>\lim(\text{IFS})</math>
+|<math>\varepsilon_0-\text{RD}</math>
+|318`4
 |-
-| [[ΩSSO]]|| \Omega Sequence System Ordinal || || <math>Y(1,3,4,2,5,8,10)</math>
+|WRO
+|Omega Remaining Ordinal
+|<math>\lim(\text{ROS})</math>
+|<math>R\ \Omega-Y</math>
+|318`4
 |-
-| [[GHO]]|| No-Go Hydra Ordinal || || <math>Y(1,3,4,3)</math>
+|SCLO
+|Small Code Lift Ordinal
+|<math>\sup(n-\text{code})</math>
+|
+|
 |-
-| [[SYO]]|| Small Yukito Ordinal || || <math>\omega-Y(1,4)</math>
+|EHO
+|Huge Hydra Ordinal
+|<math>\lim(\text{pfffz})</math>
+|
+|夏夜星空
 |-
-| MHO/ωYO|| Medium Hydra Ordinal || || <math>\omega-Y</math> 极限
+|ROO
+|Remaining Omega Ordinal
+|<math>R_\omega\text{ remaining}</math>
+|
+|318`4
 |-
-| [[CKO]]|| Church-Kleene Ordinal || <math>\omega_{1}^{CK}</math>
+|UHO
+|Ultimate Hydra Ordinal
+|<math>\lim(\text{RSAM})</math>
+|
+|夏夜星空
 |-
-| [[FUO]] || First Uncountable Ordinal || <math>\omega_{1}</math>||
+|IHO
+|Infinite Hydra Ordinal
+|<math>\lim(\text{SAM})</math>
+|
+|夏夜星空
 |}
+本表取自 [https://docs.qq.com/sheet/DSnFWckliSU5TTE15 Worldly Sheet]：<blockquote>- （SCO/CO/LCO/HCO）谁起不重要，重要的是这是纪念康托尔的，如果没有他所有gggist今天(甚至永远)都走不到一起”
+- 你们怎么把它弄成这样了，至少必要的（比如lim fffz/lim X-Y还是要的吧）
+- fffz和X-Y公认理想之前搞这么多名字有什么用
+- 不然MHO以上全都写成n-RD？- 不对 - 3184为什么要保留他造了那么多没用的序数缩写的黑历史？(bushi) - 不如还是加上 毕竟fatalis的SHO/MHO/LHO都有了</blockquote>
+==== DNAO ====
+DNAO（Disgusting Nonsense Annoyance Ordinal）
+定义：
+ (0)(1,1,1)(2,2,2)(3,3,3)(3,3,0)(4,4,1)(5,5,2)(6,6,2)(7,7,0)(8,8,1)(9,9,2)(10,9,2)(11,9,0)(12,10,1)(13,11,2)(13,11,2)(13,11,1)(14,12,2)(14,11,1)(15,12,2)(15,11,1)(16,12,0)(17,13,1)(18,14,2)(18,14,2)(18,14,1)(19,15,2)(19,14,1)(20,15,2)(20,14,1)(21,15,0)(22,16,1)(23,17,2)(23,17,2)(23,17,1)(24,18,2)(24,17,1)(25,18,2)(25,17,0)(26,18,1)(27,19,2)(27,19,2)(27,19,1)(28,20,2)(28,19,1)(29,20,2)(29,19,0)(30,20,1)(31,21,2)(31,21,2)(31,21,1)(32,22,2)(32,21,1)(33,22,2)(33,21,0)(34,22,1)(35,23,2)(35,23,2)(35,23,1)(36,24,2)(36,23,1)(37,24,2)(37,23,0)(38,24,1)(39,25,2)(40,25,2)(40,25,1)(41,26,2)(41,22,1)(42,23,2)(42,23,2)(42,23,1)(43,24,2)(43,23,1)(44,24,2)(44,23,0)(45,24,1)(46,25,2)(47,25,2)(47,25,1)(48,26,1)(49,27,0)(50,28,1)(51,29,2)(52,29,2)(52,29,1)(53,30,0)(54,31,1)(55,32,2)(56,32,2)(56,32,0)(57,33,1)(58,34,2)(59,34,2)(59,34,0)(60,35,1)(61,36,2)(62,36,2)(62,36,0)(63,37,1)(64,38,2)(65,38,2)(65,38,0)(66,39,1)(67,40,2)(68,40,2)(68,40,0)(69,41,1)(70,42,2)(71,42,2)(71,42,0)(72,43,1)(73,44,0)(74,45,1)(75,44,0)(76,45,1)(77,46,0)(78,47,0)(79,44,0)(80,45,1)(81,46,0)(82,47,0)(83,44,0)(84,45,1)(85,46,0)(86,47,0)(87,44,0)(88,45,1)(89,46,0)(90,47,0)(91,44,0)(92,45,1)(93,46,0)(94,47,0)(95,44,0)(96,45,1)(96,45,1)(96,45,1)(96,45,0)(97,46,0)(98,47,0)(99,48,0)(100,47,0)(101,48,0)(102,47,0)(103,48,0)(104,47,0)(105,48,0)(106,47,0)(107,48,0)(108,45,0)(109,46,0)(110,47,0)(111,47,0)(111,47,0)(111,47,0)(111,47,0)(111,47,0)(111,47,0)(111,46,0)(112,47,0)(113,47,0)(113,47,0)(113,47,0)(113,47,0)(113,47,0)(113,47,0)(113,46,0)(114,47,0)(115,46,0)(116,47,0)(117,46,0)(118,47,0)(119,46,0)(120,45,0)(121,46,0)(122,47,0)(123,47,0)(123,47,0)(123,47,0)(123,47,0)(123,47,0)(123,47,0)(123,46,0)(124,47,0)(125,47,0)(125,47,0)(125,47,0)(125,47,0)(125,47,0)(125,47,0)(125,46,0)(126,47,0)(127,46,0)(128,47,0)(129,46,0)(130,47,0)(131,46,0)(132,45,0)(133,46,0)(134,47,0)(135,47,0)(135,47,0)(135,47,0)(135,47,0)(135,47,0)(135,47,0)(135,46,0)(136,47,0)(137,47,0)(137,47,0)(137,47,0)(137,47,0)(137,47,0)(137,47,0)(137,46,0)(138,47,0)(139,46,0)(140,47,0)(141,46,0)(142,47,0)(143,46,0)(144,45,0)(145,46,0)(146,47,0)(147,47,0)(147,47,0)(147,47,0)(147,47,0)(147,47,0)(147,47,0)(147,46,0)(147,46,0)(147,46,0)(147,46,0)(147,46,0)(147,45,0)(148,46,0)(148,45,0)(149,46,0)(149,45,0)(150,46,0)(150,45,0)(151,45,0)(151,45,0)(150,45,0)(151,45,0)(150,45,0)(151,45,0)(148,45,0)(149,46,0)(149,45,0)(150,46,0)(150,45,0)(151,45,0)(151,45,0)(150,45,0)(151,45,0)(150,45,0)(151,45,0)(148,45,0)(149,46,0)(149,45,0)(150,46,0)(150,45,0)(151,45,0)(151,45,0)(150,45,0)(151,45,0)(150,45,0)(151,45,0)(148,45,0)(149,45,0)(149,45,0)(148,45,0)(149,45,0)(149,45,0)(148,45,0)(149,45,0)(147,45,0)(148,46,0)(148,45,0)(149,46,0)(149,45,0)(150,46,0)(150,45,0)(151,45,0)(151,45,0)(150,45,0)(151,45,0)(148,45,0)(149,46,0)(149,45,0)(150,45,0)(150,45,0)(149,45,0)(150,45,0)(149,45,0)(150,45,0)(149,45,0)(149,45,0)(149,45,0)(146,47,0)(147,47,0)(147,47,0)(147,47,0)(147,47,0)(147,47,0)(147,47,0)(147,46,0)(147,46,0)(147,46,0)(147,46,0)(147,45,0)(148,46,0)(149,47,0)(150,47,0)(150,47,0)(150,47,0)(150,47,0)(150,47,0)(150,47,0)(150,46,0)(150,46,0)(150,46,0)(150,46,0)(150,46,0)(150,45,0)(151,46,0)(151,45,0)(152,46,0)(152,45,0)(153,46,0)(153,45,0)(154,45,0)(154,45,0)(153,45,0)(154,45,0)(153,45,0)(154,45,0)(151,45,0)(152,46,0)(152,45,0)(153,46,0)(153,45,0)(154,45,0)(154,45,0)(153,45,0)(154,45,0)(153,45,0)(154,45,0)(151,45,0)(152,46,0)(152,45,0)(153,46,0)(153,45,0)(154,45,0)(154,45,0)(153,45,0)(154,45,0)(153,45,0)(154,45,0)(151,45,0)(152,45,0)(152,45,0)(151,45,0)(152,45,0)(152,45,0)(151,45,0)(152,45,0)(150,45,0)(151,46,0)(151,45,0)(152,46,0)(152,45,0)(153,46,0)(153,45,0)(154,45,0)(154,45,0)(153,45,0)(154,45,0)(151,45,0)(152,46,0)(152,45,0)(153,45,0)(153,45,0)(152,45,0)(153,45,0)(152,45,0)(153,45,0)(152,45,0)(152,45,0)(152,45,0)(149,47,0)(150,47,0)(150,47,0)(150,47,0)(150,47,0)(150,47,0)(150,47,0)(150,46,0)(150,46,0)(150,46,0)(150,46,0)(150,45,0)(151,46,0)(152,47,0)(152,47,0)(152,47,0)(151,45,0)(152,46,0)(153,47,0)(150,45,0)(151,46,0)(152,47,0)(152,47,0)(152,47,0)(151,45,0)(152,46,0)(153,47,0)(150,45,0)(151,46,0)(152,47,0)(150,45,0)(151,46,0)(152,47,0)(150,45,0)(151,45,0)(152,45,0)(152,45,0)(151,45,0)(152,45,0)(152,45,0)(150,45,0)(149,45,0)
+=== 脚注 ===
+<references />