fa(x)=fa-1(fa-1(fa-1(…x个fa-1…(fa-1(x))…x个)…))
最末位的“ω”取“x”
例：fω+1(3)=fω(fω(3))=fω(3^3)=3↑↑↑…3^3个↑…↑↑3
g(1)≈fω(3)
g(64)≈fω+1(3)
gggg...共g(64)个g...gg(64)=g^g(64)(64)≈fω+3(2)g
g↑↑↑...g(64)个↑...g(64)(64)≈fω*2(3)
ω^ω^ω^…ω个ω^…^ω=ε0
ω^ω^ω^…ω个ω^…^(εn+1)=ε(n+1)
εεεε…ω个ε…εε0=ζ0
εεεε…ω个ε…εζn=ζ(n+1)
ζζζζ…ω个ζ…ζζ0=η0
ψ0(0)=ω
ψ0(1)=ω^ω
ψ1(0)=ε0
ψ1(1)=εε0
ψ2(0)=ζ0
ψ3(0)=η0
ψψψ…ω个ψ…ψψψ0(0)(0)…ω个(1)…(0)(0)=Γ0
ψψψ…ω个ψ…ψψψΓ0(0)(0)…ω个(1)…(0)(0)=Γ1
ΓΓΓ…ω个Γ…ΓΓΓ=β0
ψ(a,x)=ψψψ…a个ψ…ψψx(0)(0)…ω个(0)…(0)(0)
ψ(1,0,0)=Γ0
ψ(1,0,1)=ΓΓ0
ψ(1,1,0)=β0
ψ(2,0,0)=ψ(1,ω,0)
ψ(1,0,0,0)=ψ(ω,0,0)
ψ(a@n)=ψ(a,0,0,…n个0,…0,0,0)
TREE(3)<fψ(ω@ω)(3)
TREE(4)<fψ(ω@ω)+1(2)
TREE(TREE(…ω个TREE(…TREE(3))…ω个)…)))<fψ(ω@ω+1)(3)