BMS分析Part1：0~BO
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本条目展示BMS强度分析的第一部分
| BMS | Standard(BOCF) |
| (0) | 1 |
| (0)(0) | 2 |
| (0)(0)(0) | 3 |
| (0)(1) | ω = First Transfinte Ordinal |
| (0)(1)(0) | ω+1 |
| (0)(1)(0)(0) | ω+2 |
| (0)(1)(0)(1) | ω2 |
| (0)(1)(0)(1)(0) | ω2+1 |
| (0)(1)(0)(1)(0)(1) | ω3 |
| (0)(1)(1) | ω^2 |
| (0)(1)(1)(0) | ω^2+1 |
| (0)(1)(1)(0)(1) | ω^2+ω |
| (0)(1)(1)(0)(1)(0) | ω^2+ω+1 |
| (0)(1)(1)(0)(1)(0)(1) | ω^2+ω2 |
| (0)(1)(1)(0)(1)(1) | ω^2*2 |
| (0)(1)(1)(0)(1)(1)(0)(1)(1) | ω^2*3 |
| (0)(1)(1)(1) | ω^3 |
| (0)(1)(1)(1)(1) | ω^4 |
| (0)(1)(2) | ω^ω = Linear Array Ordinal |
| (0)(1)(2)(0) | ω^ω+1 |
| (0)(1)(2)(0)(1)(2) | ω^ω*2 |
| (0)(1)(2)(1) | ω^(ω+1) |
| (0)(1)(2)(1)(1) | ω^(ω+2) |
| (0)(1)(2)(1)(2) | ω^(ω2) |
| (0)(1)(2)(1)(2)(1)(2) | ω^(ω3) |
| (0)(1)(2)(2) | ω^ω^2 |
| (0)(1)(2)(2)(2) | ω^ω^3 |
| (0)(1)(2)(3) | ω^ω^ω |
| (0)(1)(2)(3)(1) | ω^(ω^ω+1) |
| (0)(1)(2)(3)(2) | ω^ω^(ω+1) |
| (0)(1)(2)(3)(3) | ω^ω^(ω^2) |
| (0)(1)(2)(3)(4) | ω^ω^ω^ω |
| (0)(1)(2)(3)(4)(5) | ω^^5 |
| (0)(1,1) | ψ(Ω) = Small Cantor's Ordinal |
| (0)(1,1)(0) | ψ(Ω)+1 |
| (0)(1,1)(0)(1,1) | ψ(Ω)*2 |
| (0)(1,1)(1) | ψ(Ω+1) |
| (0)(1,1)(1)(2) | ψ(Ω+ω) |
| (0)(1,1)(1)(2,1) | ψ(Ω+ψ(Ω)) |
| (0)(1,1)(1)(2,1)(1) | ψ(Ω+ψ(Ω)+1) |
| (0)(1,1)(1)(2,1)(2) | ψ(Ω+ψ(Ω+1)) |
| (0)(1,1)(1)(2,1)(2)(3,1) | ψ(Ω+ψ(Ω+ψ(Ω))) |
| (0)(1,1)(1,1) | ψ(Ω*2) |
| (0)(1,1)(1,1)(1) | ψ(Ω*2+1) |
| (0)(1,1)(1,1)(1)(2) | ψ(Ω*2+ω) |
| (0)(1,1)(1,1)(1)(2,1) | ψ(Ω*2+ψ(Ω)) |
| (0)(1,1)(1,1)(1)(2,1)(2,1) | ψ(Ω*2+ψ(Ω*2)) |
| (0)(1,1)(1,1)(1)(2,1)(2,1)(2) | ψ(Ω*2+ψ(Ω*2+1)) |
| (0)(1,1)(1,1)(1)(2,1)(2,1)(2)(3,1)(3,1) | ψ(Ω*2+ψ(Ω*2+ψ(Ω*2))) |
| (0)(1,1)(1,1)(1,1) | ψ(Ω*3) |
| (0)(1,1)(1,1)(1,1)(1)(2,1)(2,1)(2,1) | ψ(Ω*3+ψ(Ω*3)) |
| (0)(1,1)(1,1)(1,1)(1,1) | ψ(Ω*4) |
| (0)(1,1)(1,1)(1,1)(1,1)(1,1) | ψ(Ω*5) |
| (0)(1,1)(2) | ψ(Ω*ω) |
| (0)(1,1)(2)(1) | ψ(Ω*ω+1) |
| (0)(1,1)(2)(1)(2) | ψ(Ω*ω+ω) |
| (0)(1,1)(2)(1)(2,1) | ψ(Ω*ω+ψ(Ω)) |
| (0)(1,1)(2)(1)(2,1)(2,1) | ψ(Ω*ω+ψ(Ω*2)) |
| (0)(1,1)(2)(1)(2,1)(3) | ψ(Ω*ω+ψ(Ω*ω)) |
| (0)(1,1)(2)(1)(2,1)(3)(2) | ψ(Ω*ω+ψ(Ω*ω+1)) |
| (0)(1,1)(2)(1)(2,1)(3)(2)(3,1) | ψ(Ω*ω+ψ(Ω*ω+ψ(Ω))) |
| (0)(1,1)(2)(1,1) | ψ(Ω*(ω+1)) |
| (0)(1,1)(2)(1,1)(1) | ψ(Ω*(ω+1)+1) |
| (0)(1,1)(2)(1,1)(1)(2,1) | ψ(Ω*(ω+1)+ψ(Ω)) |
| (0)(1,1)(2)(1,1)(1)(2,1)(3)(2,1) | ψ(Ω*(ω+1)+ψ(Ω*(ω+1))) |
| (0)(1,1)(2)(1,1)(1,1) | ψ(Ω*(ω+2)) |
| (0)(1,1)(2)(1,1)(1,1)(1,1) | ψ(Ω*(ω+3)) |
| (0)(1,1)(2)(1,1)(2) | ψ(Ω*(ω2)) |
| (0)(1,1)(2)(1,1)(2)(1,1) | ψ(Ω*(ω2+1)) |
| (0)(1,1)(2)(1,1)(2)(1,1)(2) | ψ(Ω*(ω3)) |
| (0)(1,1)(2)(2) | ψ(Ω*ω^2) |
| (0)(1,1)(2)(2)(1,1) | ψ(Ω*(ω^2+1)) |
| (0)(1,1)(2)(2)(1,1)(2)(2) | ψ(Ω*ω^2*2) |
| (0)(1,1)(2)(2)(2) | ψ(Ω*ω^3) |
| (0)(1,1)(2)(3) | ψ(Ω*ω^ω) |
| (0)(1,1)(2)(3)(4) | ψ(Ω*ω^ω^ω) |
| (0)(1,1)(2)(3,1) | ψ(Ω*ψ(Ω)) |
| (0)(1,1)(2)(3,1)(3,1) | ψ(Ω*ψ(Ω*2)) |
| (0)(1,1)(2)(3,1)(4) | ψ(Ω*ψ(Ω*ω)) |
| (0)(1,1)(2)(3,1)(4)(5,1) | ψ(Ω*ψ(Ω*ψ(Ω))) |
| (0)(1,1)(2,1) | ψ(Ω^2) = Cantor's Ordinal |
| (0)(1,1)(2,1)(1) | ψ(Ω^2+1) |
| (0)(1,1)(2,1)(1)(2,1) | ψ(Ω^2+ψ(Ω)) |
| (0)(1,1)(2,1)(1)(2,1)(3,1) | ψ(Ω^2+ψ(Ω^2)) |
| (0)(1,1)(2,1)(1,1) | ψ(Ω^2+Ω) |
| (0)(1,1)(2,1)(1,1)(1,1) | ψ(Ω^2+Ω*2) |
| (0)(1,1)(2,1)(1,1)(2) | ψ(Ω^2+Ω*ω) |
| (0)(1,1)(2,1)(1,1)(2)(3,1) | ψ(Ω^2+Ω*ψ(Ω)) |
| (0)(1,1)(2,1)(1,1)(2)(3,1)(4,1) | ψ(Ω^2+Ω*ψ(Ω^2)) |
| (0)(1,1)(2,1)(1,1)(2,1) | ψ(Ω^2*2) |
| (0)(1,1)(2,1)(1,1)(2,1)(1,1) | ψ(Ω^2*2+Ω) |
| (0)(1,1)(2,1)(1,1)(2,1)(1,1)(2) | ψ(Ω^2*2+Ω*ω) |
| (0)(1,1)(2,1)(1,1)(2,1)(1,1)(2,1) | ψ(Ω^2*3) |
| (0)(1,1)(2,1)(2) | ψ(Ω^2*ω) |
| (0)(1,1)(2,1)(2)(1,1) | ψ(Ω^2*ω+Ω) |
| (0)(1,1)(2,1)(2)(1,1)(2,1) | ψ(Ω^2*(ω+1)) |
| (0)(1,1)(2,1)(2)(2) | ψ(Ω^2*ω2) |
| (0)(1,1)(2,1)(2)(3) | ψ(Ω^2*ω^2) |
| (0)(1,1)(2,1)(2)(3)(4) | ψ(Ω^2*ω^ω) |
| (0)(1,1)(2,1)(2)(3,1) | ψ(Ω^2*ψ(Ω)) |
| (0)(1,1)(2,1)(2)(3,1)(3,1) | ψ(Ω^2*ψ(Ω*2)) |
| (0)(1,1)(2,1)(2)(3,1)(4,1) | ψ(Ω^2*ψ(Ω^2)) |
| (0)(1,1)(2,1)(2)(3,1)(4,1)(4) | ψ(Ω^2*ψ(Ω^2*ω)) |
| (0)(1,1)(2,1)(2,1) | ψ(Ω^3) = Large Cantor's Ordinal |
| (0)(1,1)(2,1)(2,1)(1) | ψ(Ω^3+1) |
| (0)(1,1)(2,1)(2,1)(1)(2,1) | ψ(Ω^3+ψ(Ω)) |
| (0)(1,1)(2,1)(2,1)(1)(2,1)(3,1)(3,1) | ψ(Ω^3+ψ(Ω^3)) |
| (0)(1,1)(2,1)(2,1)(1,1) | ψ(Ω^3+Ω) |
| (0)(1,1)(2,1)(2,1)(1,1)(1,1) | ψ(Ω^3+Ω*2) |
| (0)(1,1)(2,1)(2,1)(1,1)(2) | ψ(Ω^3+Ω*ω) |
| (0)(1,1)(2,1)(2,1)(1,1)(2)(3,1) | ψ(Ω^3+Ω*ψ(Ω)) |
| (0)(1,1)(2,1)(2,1)(1,1)(2)(3,1)(4,1)(4,1) | ψ(Ω^3+Ω*ψ(Ω^3)) |
| (0)(1,1)(2,1)(2,1)(1,1)(2,1) | ψ(Ω^3+Ω^2) |
| (0)(1,1)(2,1)(2,1)(1,1)(2,1)(2,1) | ψ(Ω^3*2) |
| (0)(1,1)(2,1)(2,1)(2) | ψ(Ω^3*ω) |
| (0)(1,1)(2,1)(2,1)(2)(1,1)(2,1)(2,1) | ψ(Ω^3*(ω+1)) |
| (0)(1,1)(2,1)(2,1)(2)(2) | ψ(Ω^3*ω2) |
| (0)(1,1)(2,1)(2,1)(2)(3) | ψ(Ω^3*ω^2) |
| (0)(1,1)(2,1)(2,1)(2)(3,1) | ψ(Ω^3*ψ(Ω)) |
| (0)(1,1)(2,1)(2,1)(2)(3,1)(4,1)(4,1) | ψ(Ω^3+ψ(Ω^3)) |
| (0)(1,1)(2,1)(2,1)(2,1) | ψ(Ω^4) |
| (0)(1,1)(2,1)(2,1)(2,1)(1,1) | ψ(Ω^4+Ω) |
| (0)(1,1)(2,1)(2,1)(2,1)(2) | ψ(Ω^4*ω) |
| (0)(1,1)(2,1)(2,1)(2,1)(2,1) | ψ(Ω^5) |
| (0)(1,1)(2,1)(3) | ψ(Ω^ω) = Hyper Cantor's Ordinal |
| (0)(1,1)(2,1)(3)(1) | ψ(Ω^ω+1) |
| (0)(1,1)(2,1)(3)(1)(2) | ψ(Ω^ω+ω) |
| (0)(1,1)(2,1)(3)(1)(2,1) | ψ(Ω^ω+SCO) |
| (0)(1,1)(2,1)(3)(1)(2,1)(3,1) | ψ(Ω^ω+CO) |
| (0)(1,1)(2,1)(3)(1)(2,1)(3,1)(4) | ψ(Ω^ω+HCO) |
| (0)(1,1)(2,1)(3)(1,1) | ψ(Ω^ω+Ω) |
| (0)(1,1)(2,1)(3)(1,1)(1,1) | ψ(Ω^ω+Ω*2) |
| (0)(1,1)(2,1)(3)(1,1)(2) | ψ(Ω^ω+Ω*ω) |
| (0)(1,1)(2,1)(3)(1,1)(2)(3,1) | ψ(Ω^ω+Ω*SCO) |
| (0)(1,1)(2,1)(3)(1,1)(2,1) | ψ(Ω^ω+Ω^2) |
| (0)(1,1)(2,1)(3)(1,1)(2,1)(3) | ψ(Ω^ω*2) |
| (0)(1,1)(2,1)(3)(2) | ψ(Ω^ω*ω) |
| (0)(1,1)(2,1)(3)(2)(3,1) | ψ(Ω^ω*SCO) |
| (0)(1,1)(2,1)(3)(2,1) | ψ(Ω^(ω+1)) |
| (0)(1,1)(2,1)(3)(2,1)(2) | ψ(Ω^(ω+1)*ω) |
| (0)(1,1)(2,1)(3)(2,1)(2,1) | ψ(Ω^(ω+2)) |
| (0)(1,1)(2,1)(3)(2,1)(3) | ψ(Ω^(ω2)) |
| (0)(1,1)(2,1)(3)(2,1)(3)(2,1) | ψ(Ω^(ω2+1)) |
| (0)(1,1)(2,1)(3)(3) | ψ(Ω^(ω3)) |
| (0)(1,1)(2,1)(3)(4) | ψ(Ω^ω^2) |
| (0)(1,1)(2,1)(3)(4,1) | ψ(Ω^SCO) |
| (0)(1,1)(2,1)(3)(4,1)(5,1) | ψ(Ω^CO) |
| (0)(1,1)(2,1)(3)(4,1)(5,1)(6) | ψ(Ω^HCO) |
| (0)(1,1)(2,1)(3)(4,1)(5,1)(6)(7,1)(8,1) | ψ(Ω^ψ(Ω^HCO)) |
| (0)(1,1)(2,1)(3,1) | ψ(Ω^Ω) = Feferman-Schütte Ordinal |
| (0)(1,1)(2,1)(3,1)(1) | ψ(Ω^Ω+1) |
| (0)(1,1)(2,1)(3,1)(1)(2) | ψ(Ω^Ω+ω) |
| (0)(1,1)(2,1)(3,1)(1)(2,1) | ψ(Ω^Ω+SCO) |
| (0)(1,1)(2,1)(3,1)(1)(2,1)(3,1) | ψ(Ω^Ω+CO) |
| (0)(1,1)(2,1)(3,1)(1)(2,1)(3,1)(4) | ψ(Ω^Ω+HCO) |
| (0)(1,1)(2,1)(3,1)(1)(2,1)(3,1)(4,1) | ψ(Ω^Ω+FSO) |
| (0)(1,1)(2,1)(3,1)(1)(2,1)(3,1)(4,1)(2) | ψ(Ω^Ω+ψ(Ω^Ω+1)) |
| (0)(1,1)(2,1)(3,1)(1)(2,1)(3,1)(4,1)(2)(3,1) | ψ(Ω^Ω+ψ(Ω^Ω+SCO)) |
| (0)(1,1)(2,1)(3,1)(1)(2,1)(3,1)(4,1)(2)(3,1)(4,1) | ψ(Ω^Ω+ψ(Ω^Ω+CO)) |
| (0)(1,1)(2,1)(3,1)(1)(2,1)(3,1)(4,1)(2)(3,1)(4,1)(5) | ψ(Ω^Ω+ψ(Ω^Ω+HCO)) |
| (0)(1,1)(2,1)(3,1)(1)(2,1)(3,1)(4,1)(2)(3,1)(4,1)(5,1) | ψ(Ω^Ω+ψ(Ω^Ω+FSO)) |
| (0)(1,1)(2,1)(3,1)(1,1) | ψ(Ω^Ω+Ω) |
| (0)(1,1)(2,1)(3,1)(1,1)(1) | ψ(Ω^Ω+Ω+1) |
| (0)(1,1)(2,1)(3,1)(1,1)(1)(2,1) | ψ(Ω^Ω+Ω+SCO) |
| (0)(1,1)(2,1)(3,1)(1,1)(1)(2,1)(3,1)(4,1) | ψ(Ω^Ω+Ω+FSO) |
| (0)(1,1)(2,1)(3,1)(1,1)(1,1) | ψ(Ω^Ω+Ω*2) |
| (0)(1,1)(2,1)(3,1)(1,1)(2) | ψ(Ω^Ω+Ω*ω) |
| (0)(1,1)(2,1)(3,1)(1,1)(2)(3,1) | ψ(Ω^Ω+Ω*SCO) |
| (0)(1,1)(2,1)(3,1)(1,1)(2)(3,1)(4,1)(5,1) | ψ(Ω^Ω+Ω*FSO) |
| (0)(1,1)(2,1)(3,1)(1,1)(2,1) | ψ(Ω^Ω+Ω^2) |
| (0)(1,1)(2,1)(3,1)(1,1)(2,1)(1)(2,1) | ψ(Ω^Ω+Ω^2+SCO) |
| (0)(1,1)(2,1)(3,1)(1,1)(2,1)(1)(2,1)(3,1)(4,1) | ψ(Ω^Ω+Ω^2+FSO) |
| (0)(1,1)(2,1)(3,1)(1,1)(2,1)(1,1) | ψ(Ω^Ω+Ω^2+Ω) |
| (0)(1,1)(2,1)(3,1)(1,1)(2,1)(1,1)(1,1) | ψ(Ω^Ω+Ω^2+Ω*2) |
| (0)(1,1)(2,1)(3,1)(1,1)(2,1)(1,1)(2,1) | ψ(Ω^Ω+Ω^2*2) |
| (0)(1,1)(2,1)(3,1)(1,1)(2,1)(1,1)(2,1)(1,1)(2,1) | ψ(Ω^Ω+Ω^2*3) |
| (0)(1,1)(2,1)(3,1)(1,1)(2,1)(2) | ψ(Ω^Ω+Ω^2*ω) |
| (0)(1,1)(2,1)(3,1)(1,1)(2,1)(2)(3,1) | ψ(Ω^Ω+Ω^2*SCO) |
| (0)(1,1)(2,1)(3,1)(1,1)(2,1)(2)(3,1)(4,1)(5,1) | ψ(Ω^Ω+Ω^2*FSO) |
| (0)(1,1)(2,1)(3,1)(1,1)(2,1)(2,1) | ψ(Ω^Ω+Ω^3) |
| (0)(1,1)(2,1)(3,1)(1,1)(2,1)(2,1)(1,1) | ψ(Ω^Ω+Ω^3+Ω) |
| (0)(1,1)(2,1)(3,1)(1,1)(2,1)(2,1)(1,1)(2,1)(2,1) | ψ(Ω^Ω+Ω^3*2) |
| (0)(1,1)(2,1)(3,1)(1,1)(2,1)(2,1)(2) | ψ(Ω^Ω+Ω^3*ω) |
| (0)(1,1)(2,1)(3,1)(1,1)(2,1)(2,1)(2,1) | ψ(Ω^Ω+Ω^4) |
| (0)(1,1)(2,1)(3,1)(1,1)(2,1)(3) | ψ(Ω^Ω+Ω^ω) |
| (0)(1,1)(2,1)(3,1)(1,1)(2,1)(3)(1,1)(2,1)(3) | ψ(Ω^Ω+Ω^ω*2) |
| (0)(1,1)(2,1)(3,1)(1,1)(2,1)(3)(2) | ψ(Ω^Ω+Ω^ω*ω) |
| (0)(1,1)(2,1)(3,1)(1,1)(2,1)(3)(2,1) | ψ(Ω^Ω+Ω^(ω+1)) |
| (0)(1,1)(2,1)(3,1)(1,1)(2,1)(3)(2,1)(3) | ψ(Ω^Ω+Ω^(ω2)) |
| (0)(1,1)(2,1)(3,1)(1,1)(2,1)(3)(3) | ψ(Ω^Ω+Ω^ω^2) |
| (0)(1,1)(2,1)(3,1)(1,1)(2,1)(3)(4,1) | ψ(Ω^Ω+Ω^SCO) |
| (0)(1,1)(2,1)(3,1)(1,1)(2,1)(3)(4,1)(5,1)(6,1) | ψ(Ω^Ω+Ω^FSO) |
| (0)(1,1)(2,1)(3,1)(1,1)(2,1)(3)(4,1)(5,1)(6,1)(2) | ψ(Ω^Ω+Ω^FSO*ω) |
| (0)(1,1)(2,1)(3,1)(1,1)(2,1)(3)(4,1)(5,1)(6,1)(2,1) | ψ(Ω^Ω+Ω^(FSO+1)) |
| (0)(1,1)(2,1)(3,1)(1,1)(2,1)(3)(4,1)(5,1)(6,1)(3) | ψ(Ω^Ω+Ω^(FSO+ω))? |
| (0)(1,1)(2,1)(3,1)(1,1)(2,1)(3)(4,1)(5,1)(6,1)(4) | ψ(Ω^Ω+Ω^(FSO*ω)) |
| (0)(1,1)(2,1)(3,1)(1,1)(2,1)(3)(4,1)(5,1)(6,1)(4,1) | ψ(Ω^Ω+Ω^ψ(Ω^Ω+Ω)) |
| (0)(1,1)(2,1)(3,1)(1,1)(2,1)(3)(4,1)(5,1)(6,1)(4,1)(5,1)(6)(7,1)(8,1)(9,1) | ψ(Ω^Ω+Ω^ψ(Ω^Ω+Ω^ψ(Ω^Ω))) |
| (0)(1,1)(2,1)(3,1)(1,1)(2,1)(3)(4,1)(5,1)(6,1)(4,1)(5,1)(6)(7,1)(8,1)(9,1)(5,1) | ψ(Ω^Ω+Ω^ψ(Ω^Ω+Ω^(ψ(Ω^Ω)+1)))? |
| (0)(1,1)(2,1)(3,1)(1,1)(2,1)(3,1) | ψ(Ω^Ω*2) |
| (0)(1,1)(2,1)(3,1)(1,1)(2,1)(3,1)(1,1) | ψ(Ω^Ω*2+Ω) |
| (0)(1,1)(2,1)(3,1)(1,1)(2,1)(3,1)(1,1)(2,1) | ψ(Ω^Ω*2+Ω^2) |
| (0)(1,1)(2,1)(3,1)(1,1)(2,1)(3,1)(1,1)(2,1)(2,1) | ψ(Ω^Ω*2+Ω^3) |
| (0)(1,1)(2,1)(3,1)(1,1)(2,1)(3,1)(1,1)(2,1)(3,1) | ψ(Ω^Ω*3) |
| (0)(1,1)(2,1)(3,1)(1,1)(2,1)(3,1)(1,1)(2,1)(3,1)(1,1)(2,1)(3,1) | ψ(Ω^Ω*4) |
| (0)(1,1)(2,1)(3,1)(2) | ψ(Ω^Ω*ω) |
| (0)(1,1)(2,1)(3,1)(2)(3,1) | ψ(Ω^Ω*SCO) |
| (0)(1,1)(2,1)(3,1)(2)(3,1)(4,1) | ψ(Ω^Ω*CO) |
| (0)(1,1)(2,1)(3,1)(2)(3,1)(4,1)(5,1) | ψ(Ω^Ω*FSO) |
| (0)(1,1)(2,1)(3,1)(2)(3,1)(4,1)(5,1)(4)(5,1)(6,1)(7,1) | ψ(Ω^Ω*ψ(Ω^Ω*FSO)) |
| (0)(1,1)(2,1)(3,1)(2,1) | ψ(Ω^(Ω+1)) |
| (0)(1,1)(2,1)(3,1)(2,1)(1,1) | ψ(Ω^(Ω+1)+Ω) |
| (0)(1,1)(2,1)(3,1)(2,1)(1,1)(2,1)(3,1) | ψ(Ω^(Ω+1)+Ω^Ω) |
| (0)(1,1)(2,1)(3,1)(2,1)(1,1)(2,1)(3,1)(2,1) | ψ(Ω^(Ω+1)*2) |
| (0)(1,1)(2,1)(3,1)(2,1)(2) | ψ(Ω^(Ω+1)*ω) |
| (0)(1,1)(2,1)(3,1)(2,1)(2)(3,1) | ψ(Ω^(Ω+1)*SCO) |
| (0)(1,1)(2,1)(3,1)(2,1)(2)(3,1)(4,1)(5,1) | ψ(Ω^(Ω+1)*FSO) |
| (0)(1,1)(2,1)(3,1)(2,1)(2,1) | ψ(Ω^(Ω+2)) |
| (0)(1,1)(2,1)(3,1)(2,1)(3) | ψ(Ω^(Ω+ω)) |
| (0)(1,1)(2,1)(3,1)(2,1)(3)(4,1) | ψ(Ω^(Ω+SCO)) |
| (0)(1,1)(2,1)(3,1)(2,1)(3,1) | ψ(Ω^(Ω*2)) |
| (0)(1,1)(2,1)(3,1)(2,1)(3,1)(2,1)(3,1) | ψ(Ω^(Ω*3)) |
| (0)(1,1)(2,1)(3,1)(3) | ψ(Ω^(Ω*ω)) |
| (0)(1,1)(2,1)(3,1)(3)(4,1) | ψ(Ω^(Ω*SCO)) |
| (0)(1,1)(2,1)(3,1)(3,1) | ψ(Ω^Ω^2) = Ackerman's Ordinal |
| (0)(1,1)(2,1)(3,1)(3,1)(1,1) | ψ(Ω^Ω^2+Ω) |
| (0)(1,1)(2,1)(3,1)(3,1)(1,1)(2,1)(3)(4,1)(5,1)(6,1)(6,1) | ψ(Ω^Ω^2+Ω^ACO) |
| (0)(1,1)(2,1)(3,1)(3,1)(1,1)(2,1)(3,1) | ψ(Ω^Ω^2+Ω^Ω) |
| (0)(1,1)(2,1)(3,1)(3,1)(1,1)(2,1)(3,1)(3)(4,1)(5,1)(6,1)(6,1) | ψ(Ω^Ω^2+Ω^(Ω*ACO)) |
| (0)(1,1)(2,1)(3,1)(3,1)(1,1)(2,1)(3,1)(3,1) | ψ(Ω^Ω^2*2) |
| (0)(1,1)(2,1)(3,1)(3,1)(2)(3,1)(4,1)(5,1)(5,1) | ψ(Ω^Ω^2*ACO) |
| (0)(1,1)(2,1)(3,1)(3,1)(2,1) | ψ(Ω^(Ω^2+1)) |
| (0)(1,1)(2,1)(3,1)(3,1)(2,1)(3,1) | ψ(Ω^(Ω^2+Ω)) |
| (0)(1,1)(2,1)(3,1)(3,1)(2,1)(3,1)(4)(5,1)(6,1)(7,1)(7,1) | ψ(Ω^(Ω^2+Ω*ACO)) |
| (0)(1,1)(2,1)(3,1)(3,1)(2,1)(3,1)(3,1) | ψ(Ω^(Ω^2*2)) |
| (0)(1,1)(2,1)(3,1)(3,1)(3) | ψ(Ω^(Ω^2*ω)) |
| (0)(1,1)(2,1)(3,1)(3,1)(3)(4,1)(5,1)(6,1)(6,1) | ψ(Ω^(Ω^2*ACO)) |
| (0)(1,1)(2,1)(3,1)(3,1)(3,1) | ψ(Ω^Ω^3) |
| (0)(1,1)(2,1)(3,1)(3,1)(3,1)(3,1) | ψ(Ω^Ω^4) |
| (0)(1,1)(2,1)(3,1)(4) | ψ(Ω^Ω^ω) = Small Veblen's Ordinal |
| (0)(1,1)(2,1)(3,1)(4)(1,1) | ψ(Ω^Ω^ω+Ω) |
| (0)(1,1)(2,1)(3,1)(4)(1,1)(2,1) | ψ(Ω^Ω^ω+Ω^2) |
| (0)(1,1)(2,1)(3,1)(4)(1,1)(2,1)(2,1) | ψ(Ω^Ω^ω+Ω^3) |
| (0)(1,1)(2,1)(3,1)(4)(1,1)(2,1)(3) | ψ(Ω^Ω^ω+Ω^ω) |
| (0)(1,1)(2,1)(3,1)(4)(1,1)(2,1)(3)(4,1)(5,1)(6,1)(7) | ψ(Ω^Ω^ω+Ω^SVO) |
| (0)(1,1)(2,1)(3,1)(4)(1,1)(2,1)(3,1) | ψ(Ω^Ω^ω+Ω^Ω) |
| (0)(1,1)(2,1)(3,1)(4)(1,1)(2,1)(3,1)(4) | ψ(Ω^Ω^ω*2) |
| (0)(1,1)(2,1)(3,1)(4)(2) | ψ(Ω^Ω^ω*ω) |
| (0)(1,1)(2,1)(3,1)(4)(2,1) | ψ(Ω^(Ω^ω+1)) |
| (0)(1,1)(2,1)(3,1)(4)(2,1)(3) | ψ(Ω^(Ω^ω+ω)) |
| (0)(1,1)(2,1)(3,1)(4)(2,1)(3,1) | ψ(Ω^(Ω^ω+Ω)) |
| (0)(1,1)(2,1)(3,1)(4)(2,1)(3,1)(3)(4,1)(5,1)(6,1)(7) | ψ(Ω^(Ω^ω+Ω*SVO)) |
| (0)(1,1)(2,1)(3,1)(4)(2,1)(3,1)(3,1) | ψ(Ω^(Ω^ω+Ω^2)) |
| (0)(1,1)(2,1)(3,1)(4)(2,1)(3,1)(4) | ψ(Ω^(Ω^ω*2)) |
| (0)(1,1)(2,1)(3,1)(4)(3) | ψ(Ω^(Ω^ω*ω)) |
| (0)(1,1)(2,1)(3,1)(4)(3)(4,1)(5,1)(6,1)(7) | ψ(Ω^(Ω^ω*SVO)) |
| (0)(1,1)(2,1)(3,1)(4)(3,1) | ψ(Ω^Ω^(ω+1)) |
| (0)(1,1)(2,1)(3,1)(4)(3,1)(3,1) | ψ(Ω^Ω^(ω+2)) |
| (0)(1,1)(2,1)(3,1)(4)(3,1)(4) | ψ(Ω^Ω^(ω2)) |
| (0)(1,1)(2,1)(3,1)(4)(4) | ψ(Ω^Ω^ω^2) |
| (0)(1,1)(2,1)(3,1)(4)(5) | ψ(Ω^Ω^ω^ω) |
| (0)(1,1)(2,1)(3,1)(4)(5,1) | ψ(Ω^Ω^SCO) |
| (0)(1,1)(2,1)(3,1)(4)(5,1)(6,1)(7,1) | ψ(Ω^Ω^FSO) |
| (0)(1,1)(2,1)(3,1)(4)(5,1)(6,1)(7,1)(8) | ψ(Ω^Ω^SVO) |
| (0)(1,1)(2,1)(3,1)(4)(5,1)(6,1)(7,1)(8)(9,1)(A,1)(B,1)(C) | ψ(Ω^Ω^ψ(Ω^Ω^SVO)) |
| (0)(1,1)(2,1)(3,1)(4,1) | ψ(Ω^Ω^Ω) = Large Veblen's Ordinal = the Tank |
| (0)(1,1)(2,1)(3,1)(4,1)(1,1) | ψ(Ω^Ω^Ω+Ω) |
| (0)(1,1)(2,1)(3,1)(4,1)(1,1)(2,1)(3)(4,1)(5,1)(6,1)(7,1) | ψ(Ω^Ω^Ω+Ω^LVO) |
| (0)(1,1)(2,1)(3,1)(4,1)(1,1)(2,1)(3,1) | ψ(Ω^Ω^Ω+Ω^Ω) |
| (0)(1,1)(2,1)(3,1)(4,1)(1,1)(2,1)(3,1)(4) | ψ(Ω^Ω^Ω+Ω^Ω^ω) |
| (0)(1,1)(2,1)(3,1)(4,1)(1,1)(2,1)(3,1)(4)(5,1)(6,1)(7,1)(8,1) | ψ(Ω^Ω^Ω+Ω^Ω^LVO) |
| (0)(1,1)(2,1)(3,1)(4,1)(1,1)(2,1)(3,1)(4,1) | ψ(Ω^Ω^Ω*2) |
| (0)(1,1)(2,1)(3,1)(4,1)(2) | ψ(Ω^Ω^Ω*ω) |
| (0)(1,1)(2,1)(3,1)(4,1)(2,1) | ψ(Ω^(Ω^Ω+1)) |
| (0)(1,1)(2,1)(3,1)(4,1)(2,1)(3,1)(4,1) | ψ(Ω^(Ω^Ω*2)) |
| (0)(1,1)(2,1)(3,1)(4,1)(3) | ψ(Ω^(Ω^Ω*ω)) |
| (0)(1,1)(2,1)(3,1)(4,1)(3)(4,1)(5,1)(6,1)(7,1) | ψ(Ω^(Ω^Ω*LVO)) |
| (0)(1,1)(2,1)(3,1)(4,1)(3,1) | ψ(Ω^Ω^(Ω+1)) |
| (0)(1,1)(2,1)(3,1)(4,1)(3,1)(4) | ψ(Ω^Ω^(Ω+ω)) |
| (0)(1,1)(2,1)(3,1)(4,1)(3,1)(4,1) | ψ(Ω^Ω^(Ω*2)) |
| (0)(1,1)(2,1)(3,1)(4,1)(4) | ψ(Ω^Ω^(Ω*ω)) |
| (0)(1,1)(2,1)(3,1)(4,1)(4,1) | ψ(Ω^Ω^Ω^2) |
| (0)(1,1)(2,1)(3,1)(4,1)(4,1)(4,1) | ψ(Ω^Ω^Ω^3) |
| (0)(1,1)(2,1)(3,1)(4,1)(5) | ψ(Ω^Ω^Ω^ω) |
| (0)(1,1)(2,1)(3,1)(4,1)(5)(6,1) | ψ(Ω^Ω^Ω^SCO) |
| (0)(1,1)(2,1)(3,1)(4,1)(5)(6,1)(7,1) | ψ(Ω^Ω^Ω^FSO) |
| (0)(1,1)(2,1)(3,1)(4,1)(5)(6,1)(7,1)(8,1) | ψ(Ω^Ω^Ω^LVO) |
| (0)(1,1)(2,1)(3,1)(4,1)(5,1) | ψ(Ω^Ω^Ω^Ω) |
| (0)(1,1)(2,1)(3,1)(4,1)(5,1)(6) | ψ(Ω^Ω^Ω^Ω^ω) |
| (0)(1,1)(2,1)(3,1)(4,1)(5,1)(6,1) | ψ(Ω^Ω^Ω^Ω^Ω) |
| (0)(1,1)(2,1)(3,1)(4,1)(5,1)(6,1)(7,1) | ψ(Ω^^6) |
| (0)(1,1)(2,2) | ψ(Ω_2) = Bachmann-Howard Ordinal |
| (0)(1,1)(2,2)(1) | ψ(Ω_2+1) |
| (0)(1,1)(2,2)(1)(2,1) | ψ(Ω_2+SCO) |
| (0)(1,1)(2,2)(1)(2,1)(3,1) | ψ(Ω_2+CO) |
| (0)(1,1)(2,2)(1)(2,1)(3,2) | ψ(Ω_2+BHO) |
| (0)(1,1)(2,2)(1)(2,1)(3,2)(2)(3,1)(4,2) | ψ(Ω_2+ψ(Ω_2+BHO)) |
| (0)(1,1)(2,2)(1,1) | ψ(Ω_2+Ω) |
| (0)(1,1)(2,2)(1,1)(2,1) | ψ(Ω_2+Ω^2) |
| (0)(1,1)(2,2)(1,1)(2,1)(3)(4,1)(5,2) | ψ(Ω_2+Ω^BHO) |
| (0)(1,1)(2,2)(1,1)(2,1)(3,1) | ψ(Ω_2+Ω^Ω) |
| (0)(1,1)(2,2)(1,1)(2,2) | ψ(Ω_2+ψ_1(Ω_2)) |
| (0)(1,1)(2,2)(1,1)(2,2)(1,1) | ψ(Ω_2+ψ_1(Ω_2)+Ω) |
| (0)(1,1)(2,2)(1,1)(2,2)(1,1)(2,2) | ψ(Ω_2+ψ_1(Ω_2)*2) |
| (0)(1,1)(2,2)(2) | ψ(Ω_2+ψ_1(Ω_2+1)) |
| (0)(1,1)(2,2)(2)(3,1) | ψ(Ω_2+ψ_1(Ω_2+SCO)) |
| (0)(1,1)(2,2)(2)(3,1)(4,2) | ψ(Ω_2+ψ_1(Ω_2+BHO)) |
| (0)(1,1)(2,2)(2,1) | ψ(Ω_2+ψ_1(Ω_2+Ω)) |
| (0)(1,1)(2,2)(2,1)(3)(4,1)(5,2)(4,1)(5,2) | ψ(Ω_2+ψ_1(Ω_2+Ω^ψ(Ω_2+ψ_1(Ω_2))) |
| (0)(1,1)(2,2)(2,1)(3,1) | ψ(Ω_2+ψ_1(Ω_2+Ω^Ω)) |
| (0)(1,1)(2,2)(2,1)(3,2) | ψ(Ω_2+ψ_1(Ω_2+ψ_1(Ω_2))) |
| (0)(1,1)(2,2)(2,1)(3,2)(1) | ψ(Ω_2+ψ_1(Ω_2+ψ_1(Ω_2))+1) |
| (0)(1,1)(2,2)(2,1)(3,2)(2) | ψ(Ω_2+ψ_1(Ω_2+ψ_1(Ω_2)+1)) |
| (0)(1,1)(2,2)(2,1)(3,2)(3) | ψ(Ω_2+ψ_1(Ω_2+ψ_1(Ω_2+1))) |
| (0)(1,1)(2,2)(2,1)(3,2)(3,1)(4,2) | ψ(Ω_2+ψ_1(Ω_2+ψ_1(Ω_2+ψ_1(Ω_2)))) |
| (0)(1,1)(2,2)(2,2) | ψ(Ω_2*2) |
| (0)(1,1)(2,2)(2,2)(1,1)(2,2) | ψ(Ω_2*2+ψ_1(Ω_2)) |
| (0)(1,1)(2,2)(2,2)(1,1)(2,2)(2,2) | ψ(Ω_2*2+ψ_1(Ω_2*2)) |
| (0)(1,1)(2,2)(2,2)(2) | ψ(Ω_2*2+ψ_1(Ω_2*2+1)) |
| (0)(1,1)(2,2)(2,2)(2,1) | ψ(Ω_2*2+ψ_1(Ω_2*2+Ω)) |
| (0)(1,1)(2,2)(2,2)(2,2) | ψ(Ω_2*3) |
| (0)(1,1)(2,2)(3) | ψ(Ω_2*ω) |
| (0)(1,1)(2,2)(3,1) | ψ(Ω_2*Ω) |
| (0)(1,1)(2,2)(3,1)(4,2) | ψ(Ω_2*ψ_1(Ω_2)) |
| (0)(1,1)(2,2)(3,2) | ψ(Ω_2^2) |
| (0)(1,1)(2,2)(3,2)(2,2) | ψ(Ω_2^2+Ω_2) |
| (0)(1,1)(2,2)(3,2)(2,2)(3,1) | ψ(Ω_2^2+Ω_2*Ω) |
| (0)(1,1)(2,2)(3,2)(2,2)(3,1)(4,2)(5,2) | ψ(Ω_2^2+Ω_2*ψ_1(Ω_2^2)) |
| (0)(1,1)(2,2)(3,2)(2,2)(3,2) | ψ(Ω_2^2*2) |
| (0)(1,1)(2,2)(3,2)(3) | ψ(Ω_2^2*ω) |
| (0)(1,1)(2,2)(3,2)(3,1) | ψ(Ω_2^2*Ω) |
| (0)(1,1)(2,2)(3,2)(3,2) | ψ(Ω_2^3) |
| (0)(1,1)(2,2)(3,2)(4) | ψ(Ω_2^ω) |
| (0)(1,1)(2,2)(3,2)(4,1) | ψ(Ω_2^Ω) |
| (0)(1,1)(2,2)(3,2)(4,2) | ψ(Ω_2^Ω_2) |
| (0)(1,1)(2,2)(3,2)(4,2)(2,2) | ψ(Ω_2^Ω_2+Ω_2) |
| (0)(1,1)(2,2)(3,2)(4,2)(2,2)(3,2) | ψ(Ω_2^Ω_2+Ω_2^2) |
| (0)(1,1)(2,2)(3,2)(4,2)(2,2)(3,2)(4,1)(5,2)(6,2)(7,2) | ψ(Ω_2^Ω_2+Ω_2^ψ_1(Ω_2^Ω_2)) |
| (0)(1,1)(2,2)(3,2)(4,2)(2,2)(3,2)(4,2) | ψ(Ω_2^Ω_2*2) |
| (0)(1,1)(2,2)(3,2)(4,2)(3) | ψ(Ω_2^Ω_2*ω) |
| (0)(1,1)(2,2)(3,2)(4,2)(3,1) | ψ(Ω_2^Ω_2*Ω) |
| (0)(1,1)(2,2)(3,2)(4,2)(3,2) | ψ(Ω_2^(Ω_2+1)) |
| (0)(1,1)(2,2)(3,2)(4,2)(3,2)(4,2) | ψ(Ω_2^(Ω_2*2)) |
| (0)(1,1)(2,2)(3,2)(4,2)(4) | ψ(Ω_2^(Ω_2*ω)) |
| (0)(1,1)(2,2)(3,2)(4,2)(4,1) | ψ(Ω_2^(Ω_2*Ω)) |
| (0)(1,1)(2,2)(3,2)(4,2)(4,2) | ψ(Ω_2^Ω_2^2) |
| (0)(1,1)(2,2)(3,2)(4,2)(4,2)(4,2) | ψ(Ω_2^Ω_2^3) |
| (0)(1,1)(2,2)(3,2)(4,2)(5) | ψ(Ω_2^Ω_2^ω) |
| (0)(1,1)(2,2)(3,2)(4,2)(5,1) | ψ(Ω_2^Ω_2^Ω) |
| (0)(1,1)(2,2)(3,2)(4,2)(5,2) | ψ(Ω_2^^3) |
| (0)(1,1)(2,2)(3,2)(4,2)(5,2)(6,2) | ψ(Ω_2^^4) |
| (0)(1,1)(2,2)(3,3) | ψ(Ω_3) |
| (0)(1,1)(2,2)(3,3)(1,1) | ψ(Ω_3+Ω) |
| (0)(1,1)(2,2)(3,3)(1,1)(2,1)(3,1) | ψ(Ω_3+Ω^Ω) |
| (0)(1,1)(2,2)(3,3)(1,1)(2,2) | ψ(Ω_3+ψ_1(Ω_2)) |
| (0)(1,1)(2,2)(3,3)(2,1)(3,2)(4,3) | ψ(Ω_3+ψ_1(Ω_3)) |
| (0)(1,1)(2,2)(3,3)(2,2) | ψ(Ω_3+Ω_2) |
| (0)(1,1)(2,2)(3,3)(2,2)(3,2) | ψ(Ω_3+Ω_2^2) |
| (0)(1,1)(2,2)(3,3)(2,2)(3,3) | ψ(Ω_3+ψ_2(Ω_3)) |
| (0)(1,1)(2,2)(3,3)(3) | ψ(Ω_3+ψ_2(Ω_3+1)) |
| (0)(1,1)(2,2)(3,3)(3,1) | ψ(Ω_3+ψ_2(Ω_3+Ω)) |
| (0)(1,1)(2,2)(3,3)(3,1)(4,2)(5,3) | ψ(Ω_3+ψ_2(Ω_3+ψ_1(Ω_3))) |
| (0)(1,1)(2,2)(3,3)(3,2) | ψ(Ω_3+ψ_2(Ω_3+Ω_2)) |
| (0)(1,1)(2,2)(3,3)(3,2)(4,3) | ψ(Ω_3+ψ_2(Ω_3+ψ_2(Ω_3))) |
| (0)(1,1)(2,2)(3,3)(3,3) | ψ(Ω_3*2) |
| (0)(1,1)(2,2)(3,3)(4) | ψ(Ω_3*ω) |
| (0)(1,1)(2,2)(3,3)(4,3) | ψ(Ω_3^2) |
| (0)(1,1)(2,2)(3,3)(4,3)(4,3) | ψ(Ω_3^3) |
| (0)(1,1)(2,2)(3,3)(4,3)(5) | ψ(Ω_3^ω) |
| (0)(1,1)(2,2)(3,3)(4,3)(5,3) | ψ(Ω_3^Ω_3) |
| (0)(1,1)(2,2)(3,3)(4,4) | ψ(Ω_4) |
| (0)(1,1)(2,2)(3,3)(4,4)(5,5) | ψ(Ω_5) |
| (0)(1,1)(2,2)(3,3)(4,4)(5,5)(6,6) | ψ(Ω_6) |
| (0)(1,1,1) | ψ(Ω_ω) = Buchholz's Ordinal |