BMS分析Part2：BO~EBO：修订间差异

2025年8月20日 (三) 20:27的版本

本条目展示BMS强度分析的第二部分

BMS	Standard(BOCF)
(0)(1,1,1)	ψ(Ω_ω) = Buchholz's Ordinal
(0)(1,1,1)(0)	ψ(Ω_ω)+1
(0)(1,1,1)(1)	ψ(Ω_ω+1）
(0)(1,1,1)(1)(2,1)	ψ(Ω_ω+SCO)
(0)(1,1,1)(1)(2,1)(3,2)	ψ(Ω_ω+BHO)
(0)(1,1,1)(1)(2,1,1)	ψ(Ω_ω+BO)
(0)(1,1,1)(1)(2,1,1)(2)	ψ(Ω_ω+ψ(Ω_ω+1))
(0)(1,1,1)(1)(2,1,1)(2)(3,1,1)	ψ(Ω_ω+ψ(Ω_ω+BO)
(0)(1,1,1)(1,1)	ψ(Ω_ω+Ω)
(0)(1,1,1)(1,1)(1,1)	ψ(Ω_ω+Ω*2)
(0)(1,1,1)(1,1)(2)	ψ(Ω_ω+Ω*ω)
(0)(1,1,1)(1,1)(2)(3,1,1)	ψ(Ω_ω+Ω*BO)
(0)(1,1,1)(1,1)(2,1)	ψ(Ω_ω+Ω^2)
(0)(1,1,1)(1,1)(2,2)	ψ(Ω_ω+ψ_1(Ω_2))
(0)(1,1,1)(1,1)(2,2)(3,3)	ψ(Ω_ω+ψ_1(Ω_3))
(0)(1,1,1)(1,1)(2,2,1)	ψ(Ω_ω+ψ_1(Ω_ω))
(0)(1,1,1)(1,1)(2,2,1)(1)	ψ(Ω_ω+ψ_1(Ω_ω)+1)
(0)(1,1,1)(1,1)(2,2,1)(1,1)	ψ(Ω_ω+ψ_1(Ω_ω)+Ω)
(0)(1,1,1)(1,1)(2,2,1)(1,1)(2,2)	ψ(Ω_ω+ψ_1(Ω_ω)+ψ_1(Ω_2))
(0)(1,1,1)(1,1)(2,2,1)(1,1)(2,2,1)	ψ(Ω_ω+ψ_1(Ω_ω)*2)
(0)(1,1,1)(1,1)(2,2,1)(2)	ψ(Ω_ω+ψ_1(Ω_ω+1))
(0)(1,1,1)(1,1)(2,2,1)(2)(3,1,1)	ψ(Ω_ω+ψ_1(Ω_ω+BO))
(0)(1,1,1)(1,1)(2,2,1)(2,1)	ψ(Ω_ω+ψ_1(Ω_ω+Ω))
(0)(1,1,1)(1,1)(2,2,1)(2,2)	ψ(Ω_ω+Ω_2)
(0)(1,1,1)(1,1)(2,2,1)(2,2)(3,3,1)	ψ(Ω_ω+ψ_2(Ω_ω))
(0)(1,1,1)(1,1,1)	ψ(Ω_ω*2)
(0)(1,1,1)(1,1,1)(1,1)	ψ(Ω_ω*2+Ω)
(0)(1,1,1)(1,1,1)(1,1)(2,2,1)(2,2,1)	ψ(Ω_ω2+ψ_1(Ω_ω2))
(0)(1,1,1)(1,1,1)(1,1)(2,2,1)(2,2,1)(2,2)(3,3,1)(3,3,1)	ψ(Ω_ω2+ψ_1(Ω_ω2+ψ_2(Ω_ω*2)))
(0)(1,1,1)(1,1,1)(1,1,1)	ψ(Ω_ω*3)
(0)(1,1,1)(1,1,1)(1,1,1)(1,1,1)	ψ(Ω_ω*4)
(0)(1,1,1)(2)	ψ(Ω_ω*ω)
(0)(1,1,1)(2)(1,1)	ψ(Ω_ω*ω+Ω)
(0)(1,1,1)(2)(1,1)(2,2,1)	ψ(Ω_ω*ω+ψ_1(Ω_ω))
(0)(1,1,1)(2)(1,1)(2,2,1)(3)	ψ(Ω_ωω+ψ_1(Ω_ωω))
(0)(1,1,1)(2)(1,1)(2,2,1)(3)(2,2)	ψ(Ω_ωω+ψ_1(Ω_ωω+ψ_2(Ω_3)))
(0)(1,1,1)(2)(1,1)(2,2,1)(3)(2,2)(3,3,1)	ψ(Ω_ωω+ψ_1(Ω_ωω+ψ_2(Ω_ω)))
(0)(1,1,1)(2)(1,1,1)	ψ(Ω_ω*(ω+1))
(0)(1,1,1)(2)(1,1,1)(1,1,1)	ψ(Ω_ω*(ω+2))
(0)(1,1,1)(2)(1,1,1)(2)	ψ(Ω_ω*(ω2))
(0)(1,1,1)(2)(2)	ψ(Ω_ω*ω^2)
(0)(1,1,1)(2)(3,1)	ψ(Ω_ω*SCO)
(0)(1,1,1)(2)(3,1,1)	ψ(Ω_ω*BO)
(0)(1,1,1)(2,1)	ψ(Ω_ω*Ω)
(0)(1,1,1)(2,1)(1)	ψ(Ω_ω*Ω+1)
(0)(1,1,1)(2,1)(1,1)	ψ(Ω_ω*Ω+Ω)
(0)(1,1,1)(2,1)(1,1)(1,1)	ψ(Ω_ωΩ+Ω2)
(0)(1,1,1)(2,1)(1,1)(2,1)	ψ(Ω_ω*Ω+Ω^2)
(0)(1,1,1)(2,1)(1,1)(2,2)	ψ(Ω_ω*Ω+ψ_1(Ω_2))
(0)(1,1,1)(2,1)(1,1)(2,2,1)	ψ(Ω_ω*Ω+ψ_1(Ω_ω))
(0)(1,1,1)(2,1)(1,1)(2,2,1)(2)	ψ(Ω_ω*Ω+ψ_1(Ω_ω+1))
(0)(1,1,1)(2,1)(1,1)(2,2,1)(2,2)	ψ(Ω_ω*Ω+ψ_1(Ω_ω+Ω_2))
(0)(1,1,1)(2,1)(1,1)(2,2,1)(2,2)(3,3)	ψ(Ω_ω*Ω+ψ_1(Ω_ω+ψ_2(Ω_3))
(0)(1,1,1)(2,1)(1,1)(2,2,1)(2,2)(3,3,1)	ψ(Ω_ω*Ω+ψ_1(Ω_ω+ψ_2(Ω_ω))
(0)(1,1,1)(2,1)(1,1)(2,2,1)(2,2,1)	ψ(Ω_ωΩ+ψ_1(Ω_ω2))
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3)	ψ(Ω_ωΩ+ψ_1(Ω_ωω))
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)	ψ(Ω_ωΩ+ψ_1(Ω_ωΩ))
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2)	ψ(Ω_ωΩ+ψ_1(Ω_ωΩ+1))
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,1)	ψ(Ω_ωΩ+ψ_1(Ω_ωΩ+Ω))
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,1)(3,2,1)	ψ(Ω_ωΩ+ψ_1(Ω_ωΩ+ψ_2(Ω_ω)))
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,1)(3,2,1)(4,1)	ψ(Ω_ωΩ+ψ_1(Ω_ωΩ+ψ_2(Ω_ω*Ω)))
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,2)	ψ(Ω_ω*Ω+Ω_2)
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,2)(3,3)	ψ(Ω_ω*Ω+ψ_2(Ω_3))
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,2)(3,3,1)	ψ(Ω_ω*Ω+ψ_2(Ω_ω))
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,2)(3,3,1)(3,3)	ψ(Ω_ω*Ω+ψ_2(Ω_ω+Ω_3))
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,2)(3,3,1)(3,3,1)	ψ(Ω_ωΩ+ψ_2(Ω_ω2))
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,2)(3,3,1)(4)	ψ(Ω_ωΩ+ψ_2(Ω_ωω))
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,2)(3,3,1)(4,1)	ψ(Ω_ωΩ+ψ_2(Ω_ωΩ))
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,2)(3,3,1)(4,1)(3,3)	ψ(Ω_ω*Ω+Ω_3)
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,2,1)	ψ(Ω_ω*(Ω+1))
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,2,1)(1,1)	ψ(Ω_ω*(Ω+1)+Ω)
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,2,1)(1,1)(2,2,1)(3,1)(2,2,1)	ψ(Ω_ω(Ω+1)+ψ_1(Ω_ω(Ω+1)))
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,2,1)(2)	ψ(Ω_ω(Ω+1)+ψ_1(Ω_ω(Ω+1)+1))
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,2,1)(2,1)	ψ(Ω_ω(Ω+1)+ψ_1(Ω_ω(Ω+1)+Ω))
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,2,1)(2,1)(3,2,1)(4,1)(3,2,1)	ψ(Ω_ω(Ω+1)+ψ_1(Ω_ω(Ω+1)+ψ_1(Ω_ω*(Ω+1)))
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,2,1)(2,2)	ψ(Ω_ω*(Ω+1)+Ω_2)
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,2,1)(2,2)(3,3,1)(4,1)(3,3,1)	ψ(Ω_ω*(Ω+1)+Ω_3)
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,2,1)(2,2,1)	ψ(Ω_ω*(Ω+2))
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,2,1)(2,2,1)(2,2,1)	ψ(Ω_ω*(Ω+3))
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,2,1)(3)	ψ(Ω_ω*(Ω+ω))
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,2,1)(3,1)	ψ(Ω_ωΩ2))
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(3)	ψ(Ω_ωΩω))
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(3,1)	ψ(Ω_ω*Ω^2))
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(4)	ψ(Ω_ω*Ω^ω))
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(4,2)	ψ(Ω_ω*ψ_1(Ω_2))
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(4,2,1)	ψ(Ω_ω*ψ_1(Ω_ω))
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(4,2,1)(5,1)	ψ(Ω_ωψ_1(Ω_ωΩ))
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(4,2,1)(5,1)(6,2,1)	ψ(Ω_ωψ_1(Ω_ωψ_1(Ω_ω)))?
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)	ψ(Ω_ω*Ω_2)
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(1)	ψ(Ω_ω*Ω_2+1)
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(1,1)	ψ(Ω_ω*Ω_2+Ω)
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(1,1)(2,2,1)	ψ(Ω_ω*Ω_2+ψ_1(Ω_ω))
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(1,1)(2,2,1)(3,2)	ψ(Ω_ωΩ_2+ψ_1(Ω_ωΩ_2))
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2)	ψ(Ω_ωΩ_2+ψ_1(Ω_ωΩ_2+1))
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2,1)	ψ(Ω_ωΩ_2+ψ_1(Ω_ωΩ_2+Ω))
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2,2)	ψ(Ω_ω*Ω_2+Ω_2)
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2,2)(3,3,1)	ψ(Ω_ω*Ω_2+ψ_2(Ω_ω))
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2,2)(3,3,1)(4,2)	ψ(Ω_ωΩ_2+ψ_2(Ω_ωΩ_2))
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2,2)(3,3,1)(4,2)(3,3)	ψ(Ω_ω*Ω_2+Ω_3)
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2,2)(3,3,1)(4,2)(3,3,1)	ψ(Ω_ω*(Ω_2+1))
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2,2)(3,3,1)(4,2)(4)	ψ(Ω_ωΩ_2ω)
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2,2)(3,3,1)(4,2)(5,3)	ψ(Ω_ω*ψ_2(Ω_3))
(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2,2)(3,3,1)(4,3)	ψ(Ω_ω*Ω_3)
(0)(1,1,1)(2,1)(1,1,1)	ψ(Ω_ω^2) = the First Lifting Ordinal
(0)(1,1,1)(2,1)(1,1,1)(1,1)	ψ(Ω_ω^2+Ω)
(0)(1,1,1)(2,1)(1,1,1)(1,1)(2,2)	ψ(Ω_ω^2+ψ_1(Ω_2))
(0)(1,1,1)(2,1)(1,1,1)(1,1)(2,2,1)	ψ(Ω_ω^2+ψ_1(Ω_ω))
(0)(1,1,1)(2,1)(1,1,1)(1,1)(2,2,1)(3,2)	ψ(Ω_ω^2+ψ_1(Ω_ω*Ω))
(0)(1,1,1)(2,1)(1,1,1)(1,1)(2,2,1)(3,2)(2,2,1)	ψ(Ω_ω^2+ψ_1(Ω_ω^2))
(0)(1,1,1)(2,1)(1,1,1)(1,1)(2,2,1)(3,2)(2,2,1)(2,1)(3,2,1)	ψ(Ω_ω^2+ψ_1(Ω_ω^2+ψ_1(Ω_ω)))
(0)(1,1,1)(2,1)(1,1,1)(1,1)(2,2,1)(3,2)(2,2,1)(2,1)(3,2,1)(4,2)(3,2,1)	ψ(Ω_ω^2+ψ_1(Ω_ω^2+ψ_1(Ω_ω^2)))
(0)(1,1,1)(2,1)(1,1,1)(1,1)(2,2,1)(3,2)(2,2,1)(2,2)	ψ(Ω_ω^2+Ω_2)
(0)(1,1,1)(2,1)(1,1,1)(1,1)(2,2,1)(3,2)(2,2,1)(2,2)(3,3,1)	ψ(Ω_ω^2+ψ_2(Ω_ω))
(0)(1,1,1)(2,1)(1,1,1)(1,1)(2,2,1)(3,2)(2,2,1)(2,2)(3,3,1)(4,3)(3,3,1)	ψ(Ω_ω^2+ψ_2(Ω_ω^2))
(0)(1,1,1)(2,1)(1,1,1)(1,1,1)	ψ(Ω_ω^2+Ω_ω)
(0)(1,1,1)(2,1)(1,1,1)(1,1,1)(1,1,1)	ψ(Ω_ω^2+Ω_ω*2)
(0)(1,1,1)(2,1)(1,1,1)(2)	ψ(Ω_ω^2+Ω_ω*ω)
(0)(1,1,1)(2,1)(1,1,1)(2,1)	ψ(Ω_ω^2+Ω_ω*Ω)
(0)(1,1,1)(2,1)(1,1,1)(2,1)(1,1,1)	ψ(Ω_ω^2*2)
(0)(1,1,1)(2,1)(1,1,1)(2,1)(1,1,1)(2)	ψ(Ω_ω^22+Ω_ωω)
(0)(1,1,1)(2,1)(1,1,1)(2,1)(1,1,1)(2,1)	ψ(Ω_ω^22+Ω_ωΩ)
(0)(1,1,1)(2,1)(1,1,1)(2,1)(1,1,1)(2,1)(1,1,1)	ψ(Ω_ω^2*3)
(0)(1,1,1)(2,1)(2)	ψ(Ω_ω^2*ω)
(0)(1,1,1)(2,1)(2,1)	ψ(Ω_ω^2*Ω)
(0)(1,1,1)(2,1)(2,1)(1,1)(2,2,1)(3,1)(2,2,1)	ψ(Ω_ω^2*Ω+Ω_ω)
(0)(1,1,1)(2,1)(2,1)(1,1)(2,2,1)(3,1)(3,1)(2,2,1)	ψ(Ω_ω^2*(Ω+1))
(0)(1,1,1)(2,1)(2,1)(1,1)(2,2,1)(3,2)(3,2)	ψ(Ω_ω^2*Ω_2)
(0)(1,1,1)(2,1)(2,1)(1,1,1)	ψ(Ω_ω^3)
(0)(1,1,1)(2,1)(2,1)(2,1)(1,1,1)	ψ(Ω_ω^4)
(0)(1,1,1)(2,1)(3)	ψ(Ω_ω^ω)
(0)(1,1,1)(2,1)(3)(4,1,1)	ψ(Ω_ω^BO)
(0)(1,1,1)(2,1)(3,1)	ψ(Ω_ω^Ω)
(0)(1,1,1)(2,1)(3,1)(1,1)(2,2,1)(3,2)(4,2)	ψ(Ω_ω^Ω_2)
(0)(1,1,1)(2,1)(3,1)(1,1,1)	ψ(Ω_ω^Ω_ω)
(0)(1,1,1)(2,1)(3,1)(2)	ψ(Ω_ω^Ω_ω*ω)
(0)(1,1,1)(2,1)(3,1)(2,1)	ψ(Ω_ω^Ω_ω*Ω)
(0)(1,1,1)(2,1)(3,1)(2,1)(1,1,1)	ψ(Ω_ω^(Ω_ω+1))
(0)(1,1,1)(2,1)(3,1)(2,1)(2,1)(1,1,1)	ψ(Ω_ω^(Ω_ω+2))
(0)(1,1,1)(2,1)(3,1)(2,1)(3)	ψ(Ω_ω^(Ω_ω+ω))
(0)(1,1,1)(2,1)(3,1)(2,1)(3,1)(1,1,1)	ψ(Ω_ω^(Ω_ω*2))
(0)(1,1,1)(2,1)(3,1)(3)	ψ(Ω_ω^(Ω_ω*ω))
(0)(1,1,1)(2,1)(3,1)(3,1)	ψ(Ω_ω^(Ω_ω*Ω))
(0)(1,1,1)(2,1)(3,1)(3,1)(1,1,1)	ψ(Ω_ω^Ω_ω^2)
(0)(1,1,1)(2,1)(3,1)(3,1)(3,1)(1,1,1)	ψ(Ω_ω^Ω_ω^3)
(0)(1,1,1)(2,1)(3,1)(4)	ψ(Ω_ω^Ω_ω^ω)
(0)(1,1,1)(2,1)(3,1)(4,1)(1,1,1)	ψ(Ω_ω^Ω_ω^Ω_ω)
(0)(1,1,1)(2,1)(3,1)(4,1)(5,1)(1,1,1)	ψ(Ω_ω^^4)
(0)(1,1,1)(2,1)(3,2)	ψ(Ω_(ω+1)) = Takeuti-Feferman-Buchholz's Ordinal
(0)(1,1,1)(2,1)(3,2)(1)	ψ(Ω_(ω+1)+1)
(0)(1,1,1)(2,1)(3,2)(1,1)	ψ(Ω_(ω+1)+Ω)
(0)(1,1,1)(2,1)(3,2)(1,1)(2,2)	ψ(Ω_(ω+1)+ψ_1(Ω_2))
(0)(1,1,1)(2,1)(3,2)(1,1)(2,2,1)	ψ(Ω_(ω+1)+ψ_1(Ω_ω))
(0)(1,1,1)(2,1)(3,2)(1,1)(2,2,1)(3)	ψ(Ω_(ω+1)+ψ_1(Ω_ω+*ω))
(0)(1,1,1)(2,1)(3,2)(1,1)(2,2,1)(3,1)	ψ(Ω_(ω+1)+ψ_1(Ω_ω*Ω))
(0)(1,1,1)(2,1)(3,2)(1,1)(2,2,1)(3,2)	ψ(Ω_(ω+1)+ψ_1(Ω_ω*Ω_2))
(0)(1,1,1)(2,1)(3,2)(1,1)(2,2,1)(3,2)(2,2,1)	ψ(Ω_(ω+1)+ψ_1(Ω_ω^2))
(0)(1,1,1)(2,1)(3,2)(1,1)(2,2,1)(3,2)(4,3)	ψ(Ω_(ω+1)+ψ_1(Ω_(ω+1)))
(0)(1,1,1)(2,1)(3,2)(1,1)(2,2,1)(3,2)(4,3)(2,2)	ψ(Ω_(ω+1)+Ω_2)
(0)(1,1,1)(2,1)(3,2)(1,1)(2,2,1)(3,2)(4,3)(2,2)(3,3)	ψ(Ω_(ω+1)+ψ_2(Ω_2))
(0)(1,1,1)(2,1)(3,2)(1,1)(2,2,1)(3,2)(4,3)(2,2)(3,3,1)	ψ(Ω_(ω+1)+ψ_2(Ω_ω))
(0)(1,1,1)(2,1)(3,2)(1,1)(2,2,1)(3,2)(4,3)(2,2)(3,3,1)(4,3)	ψ(Ω_(ω+1)+ψ_2(Ω_ω+Ω_3))
(0)(1,1,1)(2,1)(3,2)(1,1)(2,2,1)(3,2)(4,3)(2,2)(3,3,1)(4,3)(3,3,1)	ψ(Ω_(ω+1)+ψ_2(Ω_ω^2))
(0)(1,1,1)(2,1)(3,2)(1,1)(2,2,1)(3,2)(4,3)(2,2)(3,3,1)(4,3)(5,4)	ψ(Ω_(ω+1)+ψ_2(Ω_(ω+1)))
(0)(1,1,1)(2,1)(3,2)(1,1)(2,2,1)(3,2)(4,3)(2,2)(3,3,1)(4,3)(5,4)(3,3)	ψ(Ω_(ω+1)+Ω_3)
(0)(1,1,1)(2,1)(3,2)(1,1,1)	ψ(Ω_(ω+1)+Ω_ω)
(0)(1,1,1)(2,1)(3,2)(1,1,1)(2,1)(3,2)	ψ(Ω_(ω+1)+ψω(Ω_(ω+1)))
(0)(1,1,1)(2,1)(3,2)(2)	ψ(Ω_(ω+1)+ψω(Ω_(ω+1)+1))
(0)(1,1,1)(2,1)(3,2)(2,1)	ψ(Ω_(ω+1)+ψω(Ω_(ω+1)+Ω))
(0)(1,1,1)(2,1)(3,2)(2,1)(3,2)	ψ(Ω_(ω+1)+ψω(Ω_(ω+1)*2))
(0)(1,1,1)(2,1)(3,2)(3)	ψ(Ω_(ω+1)+ψω(Ω_(ω+1)*ω))
(0)(1,1,1)(2,1)(3,2)(3,1)	ψ(Ω_(ω+1)+ψω(Ω_(ω+1)*Ω))
(0)(1,1,1)(2,1)(3,2)(3,2)	ψ(Ω_(ω+1)*2)
(0)(1,1,1)(2,1)(3,2)(4)	ψ(Ω_(ω+1)*ω)
(0)(1,1,1)(2,1)(3,2)(4,1)	ψ(Ω_(ω+1)*Ω)
(0)(1,1,1)(2,1)(3,2)(4,1)(1,1,1)	ψ(Ω_(ω+1)*Ω_ω)
(0)(1,1,1)(2,1)(3,2)(4,1)(5,2)	ψ(Ω_(ω+1)ψω(Ω_(ω+1)ω))
(0)(1,1,1)(2,1)(3,2)(4,2)	ψ(Ω_(ω+1)^2)
(0)(1,1,1)(2,1)(3,2)(4,2)(4,2)	ψ(Ω_(ω+1)^3)
(0)(1,1,1)(2,1)(3,2)(4,2)(5)	ψ(Ω_(ω+1)^ω)
(0)(1,1,1)(2,1)(3,2)(4,2)(5,1)	ψ(Ω_(ω+1)^Ω)
(0)(1,1,1)(2,1)(3,2)(4,2)(5,1)(1,1,1)	ψ(Ω_(ω+1)^Ω_ω)
(0)(1,1,1)(2,1)(3,2)(4,2)(5,2)	ψ(Ω_(ω+1)^Ω_(ω+1))
(0)(1,1,1)(2,1)(3,2)(4,2)(5,2)(6,2)	ψ(Ω_(ω+1)^^3)
(0)(1,1,1)(2,1)(3,2)(4,3)	ψ(Ω_(ω+2))
(0)(1,1,1)(2,1)(3,2)(4,3)(4,3)	ψ(Ω_(ω+2)*2)
(0)(1,1,1)(2,1)(3,2)(4,3)(5)	ψ(Ω_(ω+2)*ω)
(0)(1,1,1)(2,1)(3,2)(4,3)(5,1)	ψ(Ω_(ω+2)*Ω)
(0)(1,1,1)(2,1)(3,2)(4,3)(5,1)(1,1,1)	ψ(Ω_(ω+2)*Ω_ω)
(0)(1,1,1)(2,1)(3,2)(4,3)(5,2)	ψ(Ω_(ω+2)*Ω_(ω+1))
(0)(1,1,1)(2,1)(3,2)(4,3)(5,3)	ψ(Ω_(ω+2)^2)
(0)(1,1,1)(2,1)(3,2)(4,3)(5,3)(6,3)	ψ(Ω_(ω+2)^^2)
(0)(1,1,1)(2,1)(3,2)(4,3)(5,4)	ψ(Ω_(ω+3))
(0)(1,1,1)(2,1)(3,2,1)	ψ(Ω_(ω2))
(0)(1,1,1)(2,1)(3,2,1)(1,1)	ψ(Ω_(ω2)+Ω)
(0)(1,1,1)(2,1)(3,2,1)(1,1)(2,2)	ψ(Ω_(ω2)+ψ_1(Ω_2))
(0)(1,1,1)(2,1)(3,2,1)(1,1)(2,2,1)	ψ(Ω_(ω2)+ψ_1(Ω_ω))
(0)(1,1,1)(2,1)(3,2,1)(1,1)(2,2,1)(3,2)	ψ(Ω_(ω2)+ψ_1(Ω_ω*Ω_2))
(0)(1,1,1)(2,1)(3,2,1)(1,1)(2,2,1)(3,2)(2,2,1)	ψ(Ω_(ω2)+ψ_1(Ω_ω^2))
(0)(1,1,1)(2,1)(3,2,1)(1,1)(2,2,1)(3,2)(3,2)(2,2,1)	ψ(Ω_(ω2)+ψ_1(Ω_ω^3))
(0)(1,1,1)(2,1)(3,2,1)(1,1)(2,2,1)(3,2)(4,3)	ψ(Ω_(ω2)+ψ_1(Ω_(ω+1)))
(0)(1,1,1)(2,1)(3,2,1)(1,1)(2,2,1)(3,2)(4,3,1)	ψ(Ω_(ω2)+ψ_1(Ω_(ω2)))
(0)(1,1,1)(2,1)(3,2,1)(1,1)(2,2,1)(3,2)(4,3,1)(2,2)	ψ(Ω_(ω2)+Ω_2)
(0)(1,1,1)(2,1)(3,2,1)(1,1)(2,2,1)(3,2)(4,3,1)(2,2)(3,3,1)(4,3)	ψ(Ω_(ω2)+ψ_2(Ω_ω))
(0)(1,1,1)(2,1)(3,2,1)(1,1)(2,2,1)(3,2)(4,3,1)(2,2)(3,3,1)(4,3)(5,4,1)	ψ(Ω_(ω2)+ψ_2(Ω_(ω2))
(0)(1,1,1)(2,1)(3,2,1)(1,1)(2,2,1)(3,2)(4,3,1)(2,2)(3,3,1)(4,3)(5,4,1)(3,3)	ψ(Ω_(ω2)+Ω_3)
(0)(1,1,1)(2,1)(3,2,1)(1,1,1)	ψ(Ω_(ω2)+Ω_ω)
(0)(1,1,1)(2,1)(3,2,1)(1,1,1)(1,1,1)	ψ(Ω_(ω2)+Ω_ω*2)
(0)(1,1,1)(2,1)(3,2,1)(1,1,1)(2)	ψ(Ω_(ω2)+Ω_ω*ω)
(0)(1,1,1)(2,1)(3,2,1)(1,1,1)(2,1)	ψ(Ω_(ω2)+Ω_ω*Ω)
(0)(1,1,1)(2,1)(3,2,1)(1,1,1)(2,1)(1,1,1)	ψ(Ω_(ω2)+Ω_ω^2)
(0)(1,1,1)(2,1)(3,2,1)(1,1,1)(2,1)(3,2)	ψ(Ω_(ω2)+ψω(Ω_(ω+1)))
(0)(1,1,1)(2,1)(3,2,1)(1,1,1)(2,1)(3,2,1)	ψ(Ω_(ω2)+ψω(Ω_(ω2)))
(0)(1,1,1)(2,1)(3,2,1)(2)	ψ(Ω_(ω2)+ψω(Ω_(ω2)+1))
(0)(1,1,1)(2,1)(3,2,1)(2,1)	ψ(Ω_(ω2)+ψω(Ω_(ω2)+Ω))
(0)(1,1,1)(2,1)(3,2,1)(2,1)(1,1,1)	ψ(Ω_(ω2)+ψω(Ω_(ω2)+Ω_ω))
(0)(1,1,1)(2,1)(3,2,1)(2,1)(1,1,1)(2,1)(3,2,1)	ψ(Ω_(ω2)+ψω(Ω_(ω2)*2))
(0)(1,1,1)(2,1)(3,2,1)(2,1)(3,2)	ψ(Ω_(ω2)+ψω(Ω_(ω2)+ψω(Ω_(ω+1)))
(0)(1,1,1)(2,1)(3,2,1)(2,1)(3,2,1)	ψ(Ω_(ω2)+ψω(Ω_(ω2)+ψω(Ω_(ω2)))
(0)(1,1,1)(2,1)(3,2,1)(3,1)(4,2,1)	ψ(Ω_(ω2)+ψω(Ω_(ω2)+ψω(Ω_(ω2+ψω(Ω_(ω2)))))
(0)(1,1,1)(2,1)(3,2,1)(3,2)	ψ(Ω_(ω2)+Ω_(ω+1))
(0)(1,1,1)(2,1)(3,2,1)(3,2)(4,2)	ψ(Ω_(ω2)+Ω_(ω+1)^2)
(0)(1,1,1)(2,1)(3,2,1)(3,2)(4,2)(5,2)	ψ(Ω_(ω2)+Ω_(ω+1)^Ω_(ω+1))
(0)(1,1,1)(2,1)(3,2,1)(3,2)(4,3)	ψ(Ω_(ω2)+ψ_(ω+1)(Ω_(ω+2)))
(0)(1,1,1)(2,1)(3,2,1)(3,2)(4,3,1)	ψ(Ω_(ω2)+ψ_(ω+1)(Ω_(ω2)))
(0)(1,1,1)(2,1)(3,2,1)(3,2)(4,3,1)(4,3)	ψ(Ω_(ω2)+Ω_(ω+2))
(0)(1,1,1)(2,1)(3,2,1)(3,2,1)	ψ(Ω_(ω2)*2)
(0)(1,1,1)(2,1)(3,2,1)(4)	ψ(Ω_(ω2)*ω)
(0)(1,1,1)(2,1)(3,2,1)(4,1)	ψ(Ω_(ω2)*Ω)
(0)(1,1,1)(2,1)(3,2,1)(4,1)(1,1,1)	ψ(Ω_(ω2)*Ω_ω)
(0)(1,1,1)(2,1)(3,2,1)(4,2)	ψ(Ω_(ω2)*Ω_(ω+1))
(0)(1,1,1)(2,1)(3,2,1)(4,2)(3,2)	ψ(Ω_(ω2)*Ω_(ω+1)+Ω_(ω+1))
(0)(1,1,1)(2,1)(3,2,1)(4,2)(3,2)(4,3,1)	ψ(Ω_(ω2)*Ω_(ω+1)+ψ_(ω+1)(Ω_(ω2)))
(0)(1,1,1)(2,1)(3,2,1)(4,2)(3,2)(4,3,1)(5,2)	ψ(Ω_(ω2)Ω_(ω+1)+ψ_(ω+1)(Ω_(ω2)Ω_(ω+1)))
(0)(1,1,1)(2,1)(3,2,1)(4,2)(3,2)(4,3,1)(5,2)(4,3)	ψ(Ω_(ω2)*Ω_(ω+1)+Ω_(ω+2))
(0)(1,1,1)(2,1)(3,2,1)(4,2)(3,2)(4,3,1)(5,2)(4,3,1)	ψ(Ω_(ω2)*(Ω_(ω+1)+1))
(0)(1,1,1)(2,1)(3,2,1)(4,2)(3,2)(4,3,1)(5,2)(4,3,1)(5,2)	ψ(Ω_(ω2)Ω_(ω+1)2)
(0)(1,1,1)(2,1)(3,2,1)(4,2)(3,2)(4,3,1)(5,2)(5)	ψ(Ω_(ω2)Ω_(ω+1)ω)
(0)(1,1,1)(2,1)(3,2,1)(4,2)(3,2)(4,3,1)(5,2)(5,2)	ψ(Ω_(ω2)*Ω_(ω+1)^2)
(0)(1,1,1)(2,1)(3,2,1)(4,2)(3,2)(4,3,1)(5,2)(6)	ψ(Ω_(ω2)*Ω_(ω+1)^ω)
(0)(1,1,1)(2,1)(3,2,1)(4,2)(3,2)(4,3,1)(5,2)(6,2)	ψ(Ω_(ω2)*Ω_(ω+1)^Ω_(ω+1))
(0)(1,1,1)(2,1)(3,2,1)(4,2)(3,2)(4,3,1)(5,2)(6,3)	ψ(Ω_(ω2)*ψ_(ω+1)(Ω_(ω+2)))
(0)(1,1,1)(2,1)(3,2,1)(4,2)(3,2)(4,3,1)(5,2)(6,3,1)	ψ(Ω_(ω2)*ψ_(ω+1)(Ω_(ω2)))
(0)(1,1,1)(2,1)(3,2,1)(4,2)(3,2)(4,3,1)(5,3)	ψ(Ω_(ω2)*Ω_(ω+2))
(0)(1,1,1)(2,1)(3,2,1)(4,2)(3,2)(4,3,1)(5,3)(6,4,1)(7,4)	ψ(Ω_(ω2)*Ω_(ω+3))
(0)(1,1,1)(2,1)(3,2,1)(4,2)(3,2,1)	ψ(Ω_(ω2)^2)
(0)(1,1,1)(2,1)(3,2,1)(4,2)(4,2)(3,2,1)	ψ(Ω_(ω2)^3)
(0)(1,1,1)(2,1)(3,2,1)(4,2)(5)	ψ(Ω_(ω2)^ω)
(0)(1,1,1)(2,1)(3,2,1)(4,2)(5,2)(3,2,1)	ψ(Ω_(ω2)^Ω_(ω2))
(0)(1,1,1)(2,1)(3,2,1)(4,2)(5,3)	ψ(Ω_(ω2+1))
(0)(1,1,1)(2,1)(3,2,1)(4,2)(5,3)(6,4)	ψ(Ω_(ω2+2))
(0)(1,1,1)(2,1)(3,2,1)(4,2)(5,3,1)	ψ(Ω_(ω3))
(0)(1,1,1)(2,1)(3,2,1)(4,2)(5,3,1)(6,4)(7,5,1)	ψ(Ω_(ω4))
(0)(1,1,1)(2,1,1)	ψ(Ω_(ω^2))
(0)(1,1,1)(2,1,1)(1,1)	ψ(Ω_(ω^2)+Ω)
(0)(1,1,1)(2,1,1)(1,1)(2,2)	ψ(Ω_(ω^2)+ψ_1(Ω_2))
(0)(1,1,1)(2,1,1)(1,1)(2,2,1)	ψ(Ω_(ω^2)+ψ_1(Ω_ω))
(0)(1,1,1)(2,1,1)(1,1)(2,2,1)(3,2,1)	ψ(Ω_(ω^2)+ψ_1(Ω_(ω^2)))
(0)(1,1,1)(2,1,1)(1,1)(2,2,1)(3,2,1)(2,2)	ψ(Ω_(ω^2)+Ω_2)
(0)(1,1,1)(2,1,1)(1,1)(2,2,1)(3,2,1)(2,2)(3,3,1)(4,3,1)	ψ(Ω_(ω^2)+ψ_2(Ω_(ω^2))
(0)(1,1,1)(2,1,1)(1,1,1)	ψ(Ω_(ω^2)+Ω_ω))
(0)(1,1,1)(2,1,1)(1,1,1)(2)	ψ(Ω_(ω^2)+Ω_ω*ω)
(0)(1,1,1)(2,1,1)(1,1,1)(2,1)	ψ(Ω_(ω^2)+Ω_ω*Ω)
(0)(1,1,1)(2,1,1)(1,1,1)(2,1)(3,1)	ψ(Ω_(ω^2)+Ω_ω^2)
(0)(1,1,1)(2,1,1)(1,1,1)(2,1)(3,2)	ψ(Ω_(ω^2)+ψω(Ω_(ω+1)))
(0)(1,1,1)(2,1,1)(1,1,1)(2,1)(3,2)(4,3)	ψ(Ω_(ω^2)+ψω(Ω_(ω+2)))
(0)(1,1,1)(2,1,1)(1,1,1)(2,1)(3,2,1)	ψ(Ω_(ω^2)+ψω(Ω_(ω2)))
(0)(1,1,1)(2,1,1)(1,1,1)(2,1)(3,2,1)(4,2,1)	ψ(Ω_(ω^2)+ψω(Ω_(ω^2)))
(0)(1,1,1)(2,1,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(3,2)	ψ(Ω_(ω^2)+Ω_(ω+1))
(0)(1,1,1)(2,1,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(3,2,1)	ψ(Ω_(ω^2)+Ω_(ω2))
(0)(1,1,1)(2,1,1)(1,1,1)(2,1,1)	ψ(Ω_(ω^2)*2)
(0)(1,1,1)(2,1,1)(1,1,1)(2,1,1)(1,1,1)(2,1,1)	ψ(Ω_(ω^2)*3)
(0)(1,1,1)(2,1,1)(2)	ψ(Ω_(ω^2)*ω)
(0)(1,1,1)(2,1,1)(2)(1,1,1)(2,1,1)	ψ(Ω_(ω^2)*(ω+1))
(0)(1,1,1)(2,1,1)(2)(1,1,1)(2,1,1)(2)	ψ(Ω_(ω^2)*(ω2))
(0)(1,1,1)(2,1,1)(2)(2)	ψ(Ω_(ω^2)*ω^2)
(0)(1,1,1)(2,1,1)(2)(3)	ψ(Ω_(ω^2)*ω^ω)
(0)(1,1,1)(2,1,1)(2)(3,1)	ψ(Ω_(ω^2)*SCO)
(0)(1,1,1)(2,1,1)(2)(3,1,1)	ψ(Ω_(ω^2)*BO)
(0)(1,1,1)(2,1,1)(2)(3,1,1)(4,1,1)	ψ(Ω_(ω^2)*ψ(Ω_(ω^2)))
(0)(1,1,1)(2,1,1)(2,1)	ψ(Ω_(ω^2)*Ω)
(0)(1,1,1)(2,1,1)(2,1)(1,1,1)	ψ(Ω_(ω^2)*Ω_ω)
(0)(1,1,1)(2,1,1)(2,1)(1,1,1)(1,1,1)	ψ(Ω_(ω^2)*Ω_ω+Ω_ω)
(0)(1,1,1)(2,1,1)(2,1)(1,1,1)(2,1)	ψ(Ω_(ω^2)Ω_ω+Ω_ωΩ)
(0)(1,1,1)(2,1,1)(2,1)(1,1,1)(2,1)(1,1,1)	ψ(Ω_(ω^2)*Ω_ω+Ω_ω^2)
(0)(1,1,1)(2,1,1)(2,1)(1,1,1)(2,1)(3,2)	ψ(Ω_(ω^2)*Ω_ω+ψ_ω(Ω_(ω+1)))
(0)(1,1,1)(2,1,1)(2,1)(1,1,1)(2,1)(3,2,1)(4,2,1)	ψ(Ω_(ω^2)*Ω_ω+ψ_ω(Ω_(ω^2)))
(0)(1,1,1)(2,1,1)(2,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,1)	ψ(Ω_(ω^2)Ω_ω+ψ_ω(Ω_(ω^2)Ω))
(0)(1,1,1)(2,1,1)(2,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,1)(1,1,1)	ψ(Ω_(ω^2)Ω_ω+ψ_ω(Ω_(ω^2)Ω_ω))
(0)(1,1,1)(2,1,1)(2,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,1)(3,2)	ψ(Ω_(ω^2)*Ω_ω+Ω_(ω+1))
(0)(1,1,1)(2,1,1)(2,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,1)(3,2,1)	ψ(Ω_(ω^2)*Ω_ω+Ω_(ω2))
(0)(1,1,1)(2,1,1)(2,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,1)(3,2,1)(4,2,1)	ψ(Ω_(ω^2)*(Ω_ω+1))
(0)(1,1,1)(2,1,1)(2,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,1)(3,2,1)(4,2,1)(5,1)(1,1,1)	ψ(Ω_(ω^2)Ω_ω2)
(0)(1,1,1)(2,1,1)(2,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,1)(4)	ψ(Ω_(ω^2)Ω_ωω)
(0)(1,1,1)(2,1,1)(2,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,1)(4,2,1)	ψ(Ω_(ω^2)*Ω_ω^2)
(0)(1,1,1)(2,1,1)(2,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,1)(5)	ψ(Ω_(ω^2)*Ω_ω^ω)
(0)(1,1,1)(2,1,1)(2,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,1)(6,2)	ψ(Ω_(ω^2)*ψω(Ω_(ω+1)))
(0)(1,1,1)(2,1,1)(2,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,1)(6,2,1)(7,2,1)	ψ(Ω_(ω^2)*ψω(Ω_(ω^2)))
(0)(1,1,1)(2,1,1)(2,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,2)	ψ(Ω_(ω^2)*Ω_(ω+1))
(0)(1,1,1)(2,1,1)(2,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,2)(4,2,1)	ψ(Ω_(ω^2)*Ω_(ω2))
(0)(1,1,1)(2,1,1)(2,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,2)(4,2,1)(5,2)(6,3,1)(7,3,1)(8,3)	ψ(Ω_(ω^2)*Ω_(ω2+1))
(0)(1,1,1)(2,1,1)(2,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,2)(4,2,1)(5,2)(6,3,1)(7,3,1)(8,3)(7,3,1)	ψ(Ω_(ω^2)*Ω_(ω3))
(0)(1,1,1)(2,1,1)(2,1)(1,1,1)(2,1,1)	ψ(Ω_(ω^2)^2)
(0)(1,1,1)(2,1,1)(2,1)(2)	ψ(Ω_(ω^2)^2*ω)
(0)(1,1,1)(2,1,1)(2,1)(2,1)	ψ(Ω_(ω^2)^2*Ω)
(0)(1,1,1)(2,1,1)(2,1)(2,1)(1,1,1)	ψ(Ω_(ω^2)^2*Ω_ω)
(0)(1,1,1)(2,1,1)(2,1)(2,1)(1,1,1)(2,1,1)	ψ(Ω_(ω^2)^3)
(0)(1,1,1)(2,1,1)(2,1)(2,1)(2,1)(1,1,1)(2,1,1)	ψ(Ω_(ω^2)^4)
(0)(1,1,1)(2,1,1)(2,1)(3)	ψ(Ω_(ω^2)^ω)
(0)(1,1,1)(2,1,1)(2,1)(3,1)	ψ(Ω_(ω^2)^Ω)
(0)(1,1,1)(2,1,1)(2,1)(3,1)(1,1,1)	ψ(Ω_(ω^2)^Ω_ω)
(0)(1,1,1)(2,1,1)(2,1)(3,1)(1,1,1)(2,1,1)	ψ(Ω_(ω^2)^Ω_(ω^2))
(0)(1,1,1)(2,1,1)(2,1)(3,2)	ψ(Ω_(ω^2+1))
(0)(1,1,1)(2,1,1)(2,1)(3,2,1)	ψ(Ω_(ω^2+ω))
(0)(1,1,1)(2,1,1)(2,1)(3,2,1)(4,2,1)	ψ(Ω_(ω^2*2))
(0)(1,1,1)(2,1,1)(2,1,1)	ψ(Ω_(ω^3))
(0)(1,1,1)(2,1,1)(2,1,1)(2,1,1)	ψ(Ω_(ω^4))
(0)(1,1,1)(2,1,1)(3)	ψ(Ω_(ω^ω))
(0)(1,1,1)(2,1,1)(3)(4,1,1)	ψ(Ω_BO)
(0)(1,1,1)(2,1,1)(3,1)	ψ(Ω_Ω) = Bird's Ordinal
(0)(1,1,1)(2,1,1)(3,1)(1)	ψ(Ω_Ω+1)
(0)(1,1,1)(2,1,1)(3,1)(1,1)	ψ(Ω_Ω+Ω)
(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2)	ψ(Ω_Ω+ψ_1(Ω_2))
(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)	ψ(Ω_Ω+ψ_1(Ω_ω))
(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)	ψ(Ω_Ω+ψ_1(Ω_(ω^2)))
(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)	ψ(Ω_Ω+ψ_1(Ω_Ω))
(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(2,2)	ψ(Ω_Ω+Ω_2)
(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(2,2,1)	ψ(Ω_Ω+Ω_ω)
(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(2,2,1)(3,2,1)	ψ(Ω_Ω+Ω_(ω^2))
(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(2,2,1)(3,2,1)(4,1)	ψ(Ω_Ω*2)
(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(3)	ψ(Ω_Ω*ω)
(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(3,1)	ψ(Ω_Ω*Ω)
(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(3,2)	ψ(Ω_Ω*Ω_2)
(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(3,2)(2,2,1)	ψ(Ω_Ω*Ω_ω)
(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(3,2)(2,2,1)(3,2,1)(4,1)	ψ(Ω_Ω^2)
(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(3,2)(4,3)	ψ(Ω_(Ω+1))
(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(3,2)(4,3,1)	ψ(Ω_(Ω+ω))
(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(3,2)(4,3,1)(5,3,1)	ψ(Ω_(Ω+ω^2))
(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(3,2)(4,3,1)(5,3,1)(6,1)	ψ(Ω_(Ω*2))
(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(3,2,1)	ψ(Ω_(Ω*ω))
(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(3,2,1)(4,1)	ψ(Ω_(Ω^2))
(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(4)	ψ(Ω_(Ω^ω))
(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(4,1)	ψ(Ω_(Ω^Ω))
(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(5,1)	ψ(Ω_(Ω^Ω^Ω))
(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(5,2)	ψ(Ω_ψ_1(Ω_2))
(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(5,2,1)	ψ(Ω_ψ_1(Ω_ω))
(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(5,2,1)(6,2,1)(7,1)	ψ(Ω_ψ_1(Ω_Ω))
(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,2)	ψ(Ω_Ω_2)
(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,2)(2,2)(3,3,1)(4,3,1)(5,3)	ψ(Ω_Ω_3)
(0)(1,1,1)(2,1,1)(3,1)(1,1,1)	ψ(Ω_Ω_ω)
(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)	ψ(Ω_Ω_ω+ψω(Ω_ω))
(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,2,1)	ψ(Ω_Ω_ω+ψω(Ω_(ω^2)))
(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,1)	ψ(Ω_Ω_ω+ψω(Ω_Ω))
(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,1)(1,1,1)	ψ(Ω_Ω_ω+ψω(Ω_Ω_ω))
(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,1)(3,2)	ψ(Ω_Ω_ω+Ω_(ω+1))
(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,1)(3,2,1)	ψ(Ω_Ω_ω+Ω_(ω2))
(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,1)(3,2,1)(4,2,1)	ψ(Ω_Ω_ω+Ω_(ω^2))
(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,1)(3,2,1)(4,2,1)(5,1)	ψ(Ω_Ω_ω+Ω_Ω)
(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,1)(3,2,1)(4,2,1)(5,1)(1,1,1)	ψ(Ω_Ω_ω*2)
(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,1)(4)	ψ(Ω_Ω_ω*ω)
(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,1)(4,1)(1,1,1)	ψ(Ω_Ω_ω*Ω_ω)
(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,1)(4,1)(5,2)	ψ(Ω_Ω_ω*ψω(Ω_(ω+1)))
(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,1)(4,1)(5,2,1)(6,2,1)(7,1)(1,1,1)	ψ(Ω_Ω_ω*ψω(Ω_Ω_ω))
(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,1)(4,2)	ψ(Ω_Ω_ω*Ω_(ω+1))
(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,1)(4,2)(3,2,1)	ψ(Ω_Ω_ω*Ω_(ω2))
(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,1)(4,2)(3,2,1)(4,2,1)(5,1)(1,1,1)	ψ(Ω_Ω_ω^2)
(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,1)(4,2)(4)	ψ(Ω_Ω_ω^2*ω)
(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,1)(4,2)(5)	ψ(Ω_Ω_ω^ω)
(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,1)(4,2)(5,3)	ψ(Ω_(Ω_ω+1))
(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,1)(4,2)(5,3,1)	ψ(Ω_(Ω_ω+ω))
(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,3,1)(7,1)(1,1,1)	ψ(Ω_(Ω_ω*2))
(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,1)(4,2,1)	ψ(Ω_(Ω_ω*ω))
(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,1)(4,2,1)(5,1)(1,1,1)	ψ(Ω_(Ω_ω^2))
(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,1)(5)	ψ(Ω_(Ω_ω^ω))
(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,1)(5,1)(1,1,1)	ψ(Ω_(Ω_ω^Ω_ω))
(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,1)(6,2)	ψ(Ω_ψω(Ω_(ω+1)))
(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,1)(6,2,1)(7,2,1)(8,1)(1,1,1)	ψ(Ω_ψω(Ω_Ω_ω))
(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,2)	ψ(Ω_Ω_(ω+1))
(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,2)(3,2,1)	ψ(Ω_Ω_(ω2))
(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,2)(3,2,1)(4,2)(5,3,1)(6,3,1)(7,3)	ψ(Ω_Ω_(ω2+1))
(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,2)(3,2,1)(4,2)(5,3,1)(6,3,1)(7,3)(5,3,1)	ψ(Ω_Ω_(ω3))
(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1,1)	ψ(Ω_Ω_(ω^2))
(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1,1)(3)	ψ(Ω_Ω_(ω^ω))
(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1,1)(3)(4,1,1)	ψ(Ω_Ω_BO)
(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1,1)(3,1)	ψ(Ω_Ω_Ω)
(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1,1)(3,1)(1,1,1)	ψ(Ω_Ω_Ω_ω)
(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1,1)(3,1)	ψ(Ω_Ω_Ω_Ω)
(0)(1,1,1)(2,1,1)(3,1)(2)	ψ(I) = Extented Buchholz's Ordinal

2025年8月20日 (三) 20:26的版本查看源代码 Z（留言 \| 贡献）监督员、管理员 617次编辑无编辑摘要标签：可视化编辑 ←上一编辑	2025年8月20日 (三) 20:27的版本查看源代码 Z（留言 \| 贡献）监督员、管理员 617次编辑小 Z移动页面BMS分析Part2：BO~0 111 211至BMS分析Part2：BO~EBO 下一编辑→
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