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本条目展示[[Bashicu矩阵|BMS]]强度分析的第一部分 {| class="wikitable" |BMS |Standard([[序数坍缩函数#BOCF|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 |} [[分类:分析]]
返回
BMS分析Part1：0~BO
。
查看“︁BMS分析Part1：0~BO”︁的源代码
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