BMS分析Part1：0~BO：修订间差异

←上一编辑下一编辑→

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2025年8月20日 (三) 19:29的版本

本条目展示BMS强度分析的第一部分

$\emptyset = 0$

$(0) = 1$

$(0) (0) = 2$

$(0) (0) (0) = 3$

$(0) (1) = (0) (0) (0) (0) (0) . . . = ω$

$(0) (1) (0) = ω + 1$

$(0) (1) (0) (0) = ω + 2$

$(0) (1) (0) (1) = ω \times 2$

$(0) (1) (0) (1) (0) (1) = ω \times 3$

$(0) (1) (1) = (0) (1) (0) (1) (0) (1) . . . = ω^{2}$

$(0) (1) (1) (0) = ω^{2} + 1$

$(0) (1) (1) (0) (1) = ω^{2} + ω$

$(0) (1) (1) (0) (1) (0) (1) = ω^{2} + ω \times 2$

$(0) (1) (1) (0) (1) (1) = ω^{2} \times 2$

$(0) (1) (1) (0) (1) (1) (0) (1) = ω^{2} \times 2 + ω$

$(0) (1) (1) (0) (1) (1) (0) (1) (1) = ω^{2} \times 3$

$(0) (1) (1) (1) = ω^{3}$

$(0) (1) (1) (1) (1) = ω^{4}$

$(0) (1) (2) = (0) (1) (1) (1) (1) . . . = ω^{ω}$

$(0) (1) (2) (0) (1) (2) = ω^{ω} \times 2$

$(0) (1) (2) (1) = ω^{ω + 1}$

$(0) (1) (2) (1) (1) = ω^{ω + 2}$

$(0) (1) (2) (1) (1) (1) = ω^{ω + 3}$

$(0) (1) (2) (1) (2) = ω^{ω \times 2}$

$(0) (1) (2) (1) (2) (1) (2) = ω^{ω \times 3}$

$(0) (1) (2) (2) = ω^{ω^{2}}$

$(0) (1) (2) (2) (1) = ω^{ω^{2} + 1}$

$(0) (1) (2) (2) (1) (2) = ω^{ω^{2} + ω}$

$(0) (1) (2) (2) (1) (2) (2) = ω^{ω^{2} \times 2}$

$(0) (1) (2) (2) (1) (2) (2) (1) (2) (2) = ω^{ω^{2} \times 3}$

$(0) (1) (2) (2) (2) = ω^{ω^{3}}$

$(0) (1) (2) (2) (2) (2) = ω^{ω^{4}}$

$(0) (1) (2) (3) = (0) (1) (2) (2) (2) (2) . . . = ω^{ω^{ω}}$

$(0) (1) (2) (3) (4) = ω^{ω^{ω^{ω}}}$

$(0) (1) (2) (3) (4) (5) = ω^{ω^{ω^{ω^{ω}}}}$

$(0) (1, 1) = (0) (1) (2) (3) (4) (5) (6) . . . = ε_{0}$

BMS	Veblen	MOCF
$(0) (1, 1)$	$ε_{0}$	$ψ (0)$
$(0) (1, 1) (0, 0)$	$ε_{0} + 1$
$(0) (1, 1) (0, 0) (1, 0)$	$ε_{0} + ω$
$(0) (1, 1) (0, 0) (1, 1)$	$ε_{0} \times 2$
$(0) (1, 1) (0, 0) (1, 1) (0, 0) (1, 1)$	$ε_{0} \times 3$
$(0) (1, 1) (1, 0)$	$ε_{0} \times ω$
$(0) (1, 1) (1, 0) (1, 0)$	$ε_{0} \times ω^{2}$
$(0) (1, 1) (1, 0) (2, 0)$	$ε_{0} \times ω^{ω}$
$(0) (1, 1) (1, 0) (2, 0) (3, 0)$	$ε_{0} \times ω^{ω^{ω}}$
$(0) (1, 1) (1, 0) (2, 1)$	$ε_{0}^{2}$
$(0) (1, 1) (1, 0) (2, 1) (1, 0) (2, 0)$	$ε_{0}^{2} \times ω$
$(0) (1, 1) (1, 0) (2, 1) (1, 0) (2, 0) (3, 0)$	$ε_{0}^{2} \times ω^{ω}$
$(0) (1, 1) (1, 0) (2, 1) (1, 0) (2, 1)$	$ε_{0}^{3}$
$(0) (1, 1) (1, 0) (2, 1) (1, 0) (2, 1) (1, 0) (2, 1)$	$ε_{0}^{4}$
$(0) (1, 1) (1, 0) (2, 1) (2, 0)$	$ε_{0}^{ω}$
$(0) (1, 1) (1, 0) (2, 1) (2, 0) (1, 0) (2, 1)$	$ε_{0}^{ω + 1}$
$(0) (1, 1) (1, 0) (2, 1) (2, 0) (1, 0) (2, 1) (1, 0) (2, 1)$	$ε_{0}^{ω + 2}$
$(0) (1, 1) (1, 0) (2, 1) (2, 0) (1, 0) (2, 1) (2, 0)$	$ε_{0}^{ω \times 2}$
$(0) (1, 1) (1, 0) (2, 1) (2, 0) (1, 0) (2, 1) (2, 0) (1, 0) (2, 1) (2, 0)$	$ε_{0}^{ω \times 3}$
$(0) (1, 1) (1, 0) (2, 1) (2, 0) (2, 0)$	$ε_{0}^{ω^{2}}$
$(0) (1, 1) (1, 0) (2, 1) (2, 0) (3, 0)$	$ε_{0}^{ω^{ω}}$
$(0) (1, 1) (1, 0) (2, 1) (2, 0) (3, 0) (4, 0)$	$ε_{0}^{ω^{ω^{ω}}}$
$(0) (1, 1) (1, 0) (2, 1) (2, 0) (3, 1)$	$ε_{0}^{ε_{0}}$
$(0) (1, 1) (1, 0) (2, 1) (2, 0) (3, 1) (3, 0) (4, 1)$	$ε_{0}^{ε_{0}^{ε_{0}}}$
$(0) (1, 1) (1, 0) (2, 1) (2, 0) (3, 1) (3, 0) (4, 1) (4, 0) (5, 1)$	$ε_{0}^{ε_{0}^{ε_{0}^{ε_{0}}}}$
$(0) (1, 1) (1, 1)$	$ε_{1}$	$ψ (1)$
$(0) (1, 1) (1, 1) (0, 0) (1, 1) (1, 1)$	$ε_{1} \times 2$
$(0) (1, 1) (1, 1) (1, 0)$	$ε_{1} \times ω$
$(0) (1, 1) (1, 1) (1, 0) (2, 1)$	$ε_{1} \times ε_{0}$
$(0) (1, 1) (1, 1) (1, 0) (2, 1) (2, 0) (3, 1)$	$ε_{1} \times ε_{0}^{2}$
$(0) (1, 1) (1, 1) (1, 0) (2, 1) (2, 0) (3, 1) (3, 0) (4, 1)$	$ε_{1} \times ε_{0}^{ε_{0}}$
$(0) (1, 1) (1, 1) (1, 0) (2, 1) (2, 1)$	$ε_{1}^{2}$
$(0) (1, 1) (1, 1) (1, 0) (2, 1) (2, 1) (2, 0)$	$ε_{1}^{ω}$
$(0) (1, 1) (1, 1) (1, 0) (2, 1) (2, 1) (2, 0) (3, 1)$	$ε_{1}^{ε_{0}}$
$(0) (1, 1) (1, 1) (1, 0) (2, 1) (2, 1) (2, 0) (3, 1) (3, 1)$	$ε_{1}^{ε_{1}}$
$(0) (1, 1) (1, 1) (1, 0) (2, 1) (2, 1) (2, 0) (3, 1) (3, 1) (3, 0) (4, 1) (4, 1)$	$ε_{1}^{ε_{1}^{ε_{1}}}$
$(0) (1, 1) (1, 1) (1, 1)$	$ε_{2}$	$ψ (2)$
$(0) (1, 1) (1, 1) (1, 1) (1, 1)$	$ε_{3}$	$ψ (3)$
$(0) (1, 1) (2, 0)$	$ε_{ω}$	$ψ (ω)$
$(0) (1, 1) (2, 0) (1, 0)$	$ε_{ω} \times ω$
$(0) (1, 1) (2, 0) (1, 0) (2, 1)$	$ε_{ω} \times ε_{0}$
$(0) (1, 1) (2, 0) (1, 0) (2, 1) (2, 1)$	$ε_{ω} \times ε_{1}$
$(0) (1, 1) (2, 0) (1, 0) (2, 1) (2, 1) (2, 1)$	$ε_{ω} \times ε_{2}$
$(0) (1, 1) (2, 0) (1, 0) (2, 1) (2, 1) (2, 1) (2, 1)$	$ε_{ω} \times ε_{3}$
$(0) (1, 1) (2, 0) (1, 0) (2, 1) (3, 0)$	$ε_{ω}^{2}$
$(0) (1, 1) (2, 0) (1, 0) (2, 1) (3, 0) (2, 0) (3, 1) (4, 0)$	$ε_{ω}^{ε_{ω}}$
$(0) (1, 1) (2, 0) (1, 1)$	$ε_{ω + 1}$	$ψ (ω + 1)$
$(0) (1, 1) (2, 0) (1, 1) (1, 1)$	$ε_{ω + 2}$	$ψ (ω + 2)$
$(0) (1, 1) (2, 0) (1, 1) (1, 1) (1, 1)$	$ε_{ω + 3}$	$ψ (ω + 3)$
$(0) (1, 1) (2, 0) (1, 1) (2, 0)$	$ε_{ω \times 2}$	$ψ (ω \times 2)$
$(0) (1, 1) (2, 0) (1, 1) (2, 0) (1, 1) (2, 0)$	$ε_{ω \times 3}$	$ψ (ω \times 3)$
$(0) (1, 1) (2, 0) (2, 0)$	$ε_{ω^{2}}$	$ψ (ω^{2})$
$(0) (1, 1) (2, 0) (2, 0) (2, 0)$	$ε_{ω^{3}}$	$ψ (ω^{3})$
$(0) (1, 1) (2, 0) (3, 0)$	$ε_{ω^{ω}}$	$ψ (ω^{ω})$
$(0) (1, 1) (2, 0) (3, 0) (4, 0)$	$ε_{ω^{ω^{ω}}}$	$ψ (ω^{ω^{ω}})$
$(0) (1, 1) (2, 0) (3, 1)$	$ε_{ε_{0}}$	$ψ (ψ (0))$
$(0) (1, 1) (2, 0) (3, 1) (1, 1)$	$ε_{ε_{0} + 1}$	$ψ (ψ (0) + 1)$
$(0) (1, 1) (2, 0) (3, 1) (3, 1)$	$ε_{ε_{1}}$	$ψ (ψ (1))$
$(0) (1, 1) (2, 0) (3, 1) (4, 0)$	$ε_{ε_{ω}}$	$ψ (ψ (ω))$
$(0) (1, 1) (2, 0) (3, 1) (4, 0) (5, 1)$	$ε_{ε_{ε_{0}}}$	$ψ (ψ (ψ (0)))$
$(0) (1, 1) (2, 0) (3, 1) (4, 0) (5, 1) (6, 0) (7, 1)$	$ε_{ε_{ε_{ε_{0}}}}$	$ψ (ψ (ψ (ψ (0))))$
$(0) (1, 1) (2, 1)$	$ζ_{0}$	$ψ (Ω)$
$(0) (1, 1) (2, 1) (1, 0) (2, 1) (3, 1)$	$ζ_{0}^{2}$
$(0) (1, 1) (2, 1) (1, 0) (2, 1) (3, 1) (2, 0) (3, 1) (4, 1)$	$ζ_{0}^{ζ_{0}}$
$(0) (1, 1) (2, 1) (1, 1)$	$ε_{ζ_{0} + 1}$	$ψ (Ω + 1)$
$(0) (1, 1) (2, 1) (1, 1) (1, 0) (2, 1) (3, 1) (2, 1)$	$ε_{ζ_{0} + 1}^{2}$
$(0) (1, 1) (2, 1) (1, 1) (1, 1)$	$ε_{ζ_{0} + 2}$
$(0) (1, 1) (2, 1) (1, 1) (2, 0)$	$ε_{ζ_{0} + ω}$
$(0) (1, 1) (2, 1) (1, 1) (2, 0) (3, 1)$	$ε_{ζ_{0} + ε_{0}}$
$(0) (1, 1) (2, 1) (1, 1) (2, 0) (3, 1) (4, 1)$	$ε_{ζ_{0} \times 2}$
$(0) (1, 1) (2, 1) (1, 1) (2, 0) (3, 1) (4, 1) (3, 1)$	$ε_{ε_{ζ_{0} + 1}}$
$(0) (1, 1) (2, 1) (1, 1) (2, 0) (3, 1) (4, 1) (3, 1) (4, 0) (5, 1) (6, 1) (5, 1)$	$ε_{ε_{ε_{ζ + 1}}}$
$(0) (1, 1) (2, 1) (1, 1) (2, 1)$	$ζ_{1}$
$(0) (1, 1) (2, 1) (1, 1) (2, 1) (1, 1)$	$ε_{ζ_{1} + 1}$
$(0) (1, 1) (2, 1) (1, 1) (2, 0)$	$ε_{ζ_{1} + ω}$
$(0) (1, 1) (2, 1) (1, 1) (2, 1) (1, 1) (2, 1)$	$ζ_{2}$
$(0) (1, 1) (2, 1) (1, 1) (2, 1) (1, 1) (2, 1) (1, 1) (2, 1)$	$ζ_{3}$
$(0) (1, 1) (2, 1) (2, 0)$	$ζ_{ω}$
$(0) (1, 1) (2, 1) (2, 0) (2, 0)$	$ζ_{ω^{2}}$
$(0) (1, 1) (2, 1) (2, 0) (3, 1)$	$ζ_{ε_{0}}$
$(0) (1, 1) (2, 1) (2, 0) (3, 1) (4, 1)$	$ζ_{ζ_{0}}$
$(0) (1, 1) (2, 1) (2, 0) (3, 1) (4, 1) (4, 0) (5, 1) (6, 1)$	$ζ_{ζ_{ζ_{0}}}$
$(0) (1, 1) (2, 1) (2, 1)$	$η_{0}$
$(0) (1, 1) (2, 1) (2, 1) (1, 1)$	$ε_{η_{0} + 1}$
$(0) (1, 1) (2, 1) (2, 1) (1, 1) (2, 1)$	$ζ_{η_{0} + 1}$
$(0) (1, 1) (2, 1) (2, 1) (1, 1) (2, 1) (2, 0) (3, 1) (4, 1) (4, 1) (3, 1) (4, 1)$	$ζ_{ζ_{η_{0} + 1}}$
$(0) (1, 1) (2, 1) (2, 1) (1, 1) (2, 1) (2, 1)$	$η_{1}$
$(0) (1, 1) (2, 1) (2, 1) (1, 1) (2, 1) (2, 1) (1, 1) (2, 1) (2, 1)$	$η_{2}$
$(0) (1, 1) (2, 1) (2, 1) (2, 0)$	$η_{ω}$
$(0) (1, 1) (2, 1) (2, 1) (2, 1)$	$φ (4, 0)$	$ψ (Ω^{3})$
$(0) (1, 1) (2, 1) (3, 0)$	$φ (ω, 0)$	$ψ (Ω^{ω})$
$(0) (1, 1) (2, 1) (3, 0) (1, 1)$	$φ (1, φ (ω, 0) + 1)$	$ψ (Ω^{ω} + 1)$
$(0) (1, 1) (2, 1) (3, 0) (1, 1) (2, 1)$	$φ (2, φ (ω, 0) + 1)$	$ψ (Ω^{ω} + Ω)$
$(0) (1, 1) (2, 1) (3, 0) (1, 1) (2, 1) (2, 1)$	$φ (3, φ (ω, 0) + 1)$	$ψ (Ω^{ω} + Ω^{2})$
$(0) (1, 1) (2, 1) (3, 0) (1, 1) (2, 1) (3, 0)$	$φ (ω, 1)$	$ψ (Ω^{ω} \times 2)$
$(0) (1, 1) (2, 1) (3, 0) (1, 1) (2, 1) (3, 0) (1, 1) (2, 1) (3, 0)$	$φ (ω, 2)$	$ψ (Ω^{ω} \times 3)$
$(0) (1, 1) (2, 1) (3, 0) (2, 0)$	$φ (ω, ω)$	$ψ (Ω^{ω} \times ω)$
$(0) (1, 1) (2, 1) (3, 0) (2, 1)$	$φ (ω + 1, 0)$	$ψ (Ω^{ω + 1})$
$(0) (1, 1) (2, 1) (3, 0) (2, 1) (2, 1)$	$φ (ω + 2, 0)$	$ψ (Ω^{ω + 2})$
$(0) (1, 1) (2, 1) (3, 0) (2, 1) (2, 1) (2, 1)$	$φ (ω + 3, 0)$	$ψ (Ω^{ω + 3})$
$(0) (1, 1) (2, 1) (3, 0) (2, 1) (3, 0)$	$φ (ω \times 2, 0)$	$ψ (Ω^{ω \times 2})$
$(0) (1, 1) (2, 1) (3, 0) (2, 1) (3, 0) (2, 1) (3, 0)$	$φ (ω \times 3, 0)$	$ψ (Ω^{ω \times 3})$
$(0) (1, 1) (2, 1) (3, 0) (3, 0)$	$φ (ω^{2}, 0)$	$ψ (Ω^{ω^{2}})$
$(0) (1, 1) (2, 1) (3, 0) (4, 1)$	$φ (φ (1, 0), 0)$	$ψ (Ω^{ψ (0)})$
$(0) (1, 1) (2, 1) (3, 0) (4, 1) (5, 1)$	$φ (φ (2, 0), 0)$	$ψ (Ω^{ψ (Ω)})$
$(0) (1, 1) (2, 1) (3, 0) (4, 1) (5, 1) (6, 0)$	$φ (φ (ω, 0), 0)$	$ψ (Ω^{ψ (Ω^{ω})})$
$(0) (1, 1) (2, 1) (3, 0) (4, 1) (5, 1) (6, 0) (7, 1) (8, 1) (9, 0)$	$φ (φ (φ (ω, 0), 0), 0)$	$ψ (Ω^{ψ (Ω^{ψ (Ω^{ω})})})$
$(0) (1, 1) (2, 1) (3, 1)$	$φ (1, 0, 0) = Γ_{0}$	$ψ (Ω^{Ω})$
$(0) (1, 1) (2, 1) (3, 1) (1, 1) (2, 1) (3, 1)$	$φ (1, 0, 1) = Γ_{1}$	$ψ (Ω^{Ω} \times 2)$
$(0) (1, 1) (2, 1) (3, 1) (1, 1) (2, 1) (3, 1) (1, 1) (2, 1) (3, 1)$	$φ (1, 0, 2) = Γ_{2}$	$ψ (Ω^{Ω} \times 3)$
$(0) (1, 1) (2, 1) (3, 1) (2, 0)$	$φ (1, 0, ω) = Γ_{ω}$	$ψ (Ω^{Ω} \times ω)$
$(0) (1, 1) (2, 1) (3, 1) (2, 0) (3, 1) (4, 1) (5, 1)$	$φ (1, 0, φ (1, 0, 0)) = Γ_{Γ_{0}}$	$ψ (Ω^{Ω} \times ψ (Ω^{Ω}))$
$(0) (1, 1) (2, 1) (3, 1) (2, 0) (3, 1) (4, 1) (5, 1) (4, 0) (5, 1) (6, 1) (7, 1)$	$φ (1, 0, φ (1, 0, φ (1, 0, 0))) = Γ_{Γ_{Γ_{0}}}$	$ψ (Ω^{Ω} \times ψ (Ω^{Ω} \times ψ (Ω^{Ω})))$
$(0) (1, 1) (2, 1) (3, 1) (2, 1)$	$φ (1, 1, 0)$	$ψ (Ω^{Ω + 1})$
$(0) (1, 1) (2, 1) (3, 1) (2, 1) (2, 1)$	$φ (1, 2, 0)$	$ψ (Ω^{Ω + 2})$
$(0) (1, 1) (2, 1) (3, 1) (2, 1) (3, 0)$	$φ (1, ω, 0)$	$ψ (Ω^{Ω + ω})$
$(0) (1, 1) (2, 1) (3, 1) (2, 1) (3, 0) (4, 1) (5, 1) (6, 1) (5, 1) (6, 0)$	$φ (1, φ (1, ω, 0), 0)$	$ψ (Ω^{Ω + ψ (Ω^{Ω + ω})})$
$(0) (1, 1) (2, 1) (3, 1) (2, 1) (3, 1)$	$ψ (2, 0, 0)$	$ψ (Ω^{Ω \times 2})$
$(0) (1, 1) (2, 1) (3, 1) (2, 1) (3, 1) (2, 1) (3, 1)$	$ψ (3, 0, 0)$	$ψ (Ω^{Ω \times 3})$
$(0) (1, 1) (2, 1) (3, 1) (3, 0)$	$φ (ω, 0, 0)$	$ψ (Ω^{Ω \times ω})$
$(0) (1, 1) (2, 1) (3, 1) (3, 1)$	$φ (1, 0, 0, 0)$	$ψ (Ω^{Ω^{2}})$
$(0) (1, 1) (2, 1) (3, 1) (3, 1) (3, 1)$	$φ (1, 0, 0, 0, 0)$	$ψ (Ω^{Ω^{3}})$

BMS	MOCF
$(0) (1, 1) (2, 1) (3, 1) (4, 0)$	$ψ (Ω^{Ω^{ω}})$
$(0) (1, 1) (2, 1) (3, 1) (4, 0) (5, 1)$	$ψ (Ω^{Ω^{ψ (0)}})$
$(0) (1, 1) (2, 1) (3, 1) (4, 0) (5, 1) (6, 1)$	$ψ (Ω^{Ω^{ψ (Ω)}})$
$(0) (1, 1) (2, 1) (3, 1) (4, 0) (5, 1) (6, 1) (7, 1)$	$ψ (Ω^{Ω^{ψ (Ω^{Ω})}})$
$(0) (1, 1) (2, 1) (3, 1) (4, 1)$	$ψ (Ω^{Ω^{Ω}})$
$(0) (1, 1) (2, 1) (3, 1) (4, 1) (5, 1)$	$ψ (Ω^{Ω^{Ω^{Ω}}})$
$(0) (1, 1) (2, 2)$	$ψ (ψ_{1} (0))$
$(0) (1, 1) (2, 2) (1, 1)$	$ψ (ψ_{1} (0) + 1)$
$(0) (1, 1) (2, 2) (1, 1) (2, 1)$	$ψ (ψ_{1} (0) + Ω)$
$(0) (1, 1) (2, 2) (1, 1) (2, 1) (3, 1)$	$ψ (ψ_{1} (0) + Ω^{Ω})$
$(0) (1, 1) (2, 2) (1, 1) (2, 2)$	$ψ (ψ_{1} (0) \times 2)$
$(0) (1, 1) (2, 2) (2, 0)$	$ψ (ψ_{1} (0) \times ω)$
$(0) (1, 1) (2, 2) (2, 1)$	$ψ (ψ_{1} (0) \times Ω)$
$(0) (1, 1) (2, 2) (2, 1) (3, 0)$	$ψ (ψ_{1} (0) \times Ω^{ω})$
$(0) (1, 1) (2, 2) (2, 1) (3, 1)$	$ψ (ψ_{1} (0) \times Ω^{Ω})$
$(0) (1, 1) (2, 2) (2, 1) (3, 2)$	$ψ (ψ_{1} (0)^{2})$
$(0) (1, 1) (2, 2) (2, 1) (3, 2) (3, 0)$	$ψ (ψ_{1} (0)^{ω})$
$(0) (1, 1) (2, 2) (2, 1) (3, 2) (3, 1) (4, 2)$	$ψ (ψ_{1} (0)^{ψ_{1} (0)})$
$(0) (1, 1) (2, 2) (2, 2)$	$ψ (ψ_{1} (1))$
$(0) (1, 1) (2, 2) (3, 0)$	$ψ (ψ_{1} (ω))$
$(0) (1, 1) (2, 2) (3, 1) (4, 2)$	$ψ (ψ_{1} (ψ_{1} (0)))$
$(0) (1, 1) (2, 2) (3, 2)$	$ψ (Ω_{2})$
$(0) (1, 1) (2, 2) (3, 2) (1, 1)$	$ψ (Ω_{2} + Ω)$
$(0) (1, 1) (2, 2) (3, 2) (1, 1) (2, 2)$	$ψ (Ω_{2} + ψ_{1} (0))$
$(0) (1, 1) (2, 2) (3, 2) (1, 1) (2, 2) (3, 1) (4, 2)$	$ψ (Ω_{2} + ψ_{1} (ψ_{1} (0)))$
$(0) (1, 1) (2, 2) (3, 2) (1, 1) (2, 2) (3, 2)$	$ψ (Ω_{2} + ψ_{1} (Ω_{2}))$
$(0) (1, 1) (2, 2) (3, 2) (2, 0)$	$ψ (Ω_{2} + ψ_{1} (Ω_{2}) \times ω)$
$(0) (1, 1) (2, 2) (3, 2) (2, 1) (3, 2) (4, 2)$	$ψ (Ω_{2} + ψ_{1} (Ω_{2})^{2})$
$(0) (1, 1) (2, 2) (3, 2) (2, 1) (3, 2) (4, 2) (3, 0)$	$ψ (Ω_{2} + ψ_{1} (Ω_{2})^{ω})$
$(0) (1, 1) (2, 2) (3, 2) (2, 1) (3, 2) (4, 2) (3, 1) (4, 2) (5, 2)$	$ψ (Ω_{2} + ψ_{1} (Ω_{2})^{ψ_{1} (Ω_{2})})$
$(0) (1, 1) (2, 2) (3, 2) (2, 2)$	$ψ (Ω_{2} + ψ_{1} (Ω_{2} + 1))$
$(0) (1, 1) (2, 2) (3, 2) (2, 2) (3, 0)$	$ψ (Ω_{2} + ψ_{1} (Ω_{2} + ω))$
$(0) (1, 1) (2, 2) (3, 2) (2, 2) (3, 1) (4, 2) (5, 2)$	$ψ (Ω_{2} + ψ_{1} (Ω_{2} + ψ_{1} (Ω_{2})))$
$(0) (1, 1) (2, 2) (3, 2) (2, 2) (3, 1) (4, 2) (5, 2) (3, 0)$	$ψ (Ω_{2} + ψ_{1} (Ω_{2} + ψ_{1} (Ω_{2}) \times ω))$
$(0) (1, 1) (2, 2) (3, 2) (2, 2) (3, 1) (4, 2) (5, 2) (4, 0)$	$ψ (Ω_{2} + ψ_{1} (Ω_{2} + ψ_{1} (Ω_{2})^{ω}))$
$(0) (1, 1) (2, 2) (3, 2) (2, 2) (3, 1) (4, 2) (5, 2) (4, 1) (5, 2) (6, 2)$	$ψ (Ω_{2} + ψ_{1} (Ω_{2} + ψ_{1} (Ω_{2})^{ψ_{1} (Ω_{2})}))$
$(0) (1, 1) (2, 2) (3, 2) (2, 2) (3, 1) (4, 2) (5, 2) (4, 2)$	$ψ (Ω_{2} + ψ_{1} (Ω_{2} + ψ_{1} (Ω_{2} + 1)))$
$(0) (1, 1) (2, 2) (3, 2) (2, 2) (3, 1) (4, 2) (5, 2) (4, 2) (5, 0)$	$ψ (Ω_{2} + ψ_{1} (Ω_{2} + ψ_{1} (Ω_{2} + ω)))$
$(0) (1, 1) (2, 2) (3, 2) (2, 2) (3, 1) (4, 2) (5, 2) (4, 2) (5, 0) (5, 1) (6, 2) (7, 2)$	$ψ (Ω_{2} + ψ_{1} (Ω_{2} + ψ_{1} (Ω_{2} + ψ_{1} (Ω_{2}))))$
$(0) (1, 1) (2, 2) (3, 2) (2, 2) (3, 2)$	$ψ (Ω_{2} \times 2)$
$(0) (1, 1) (2, 2) (3, 2) (3, 0)$	$ψ (Ω_{2} \times ω)$
$(0) (1, 1) (2, 2) (3, 2) (3, 1) (4, 2) (5, 2)$	$ψ (Ω_{2} \times ψ_{1} (Ω_{2}))$
$(0) (1, 1) (2, 2) (3, 2) (3, 2)$	$ψ (Ω_{2}^{2})$
$(0) (1, 1) (2, 2) (3, 2) (4, 0)$	$ψ (Ω_{2}^{ω})$
$(0) (1, 1) (2, 2) (3, 2) (4, 2)$	$ψ (Ω_{2}^{Ω_{2}})$
$(0) (1, 1) (2, 2) (3, 3)$	$ψ (ψ_{2} (0))$
$(0) (1, 1) (2, 2) (3, 3) (4, 3)$	$ψ (Ω_{3})$
$(0) (1, 1) (2, 2) (3, 3) (4, 4)$	$ψ (ψ_{3} (0))$
$(0) (1, 1, 1) = (0) (1, 1) (2, 2) (3, 3) \dots$	$ψ (Ω_{ω})$

@@ 第79行： / 第79行： @@
 |<math>(0)(1,1)</math>
 |<math>\varepsilon_0</math>
+|<math>\psi(0)</math>
 |-
 |<math>(0)(1,1)(0,0)</math>
@@ 第154行： / 第155行： @@
 |<math>(0)(1,1)(1,1)</math>
 |<math>\varepsilon_1</math>
+|<math>\psi(1)</math>
 |-
 |<math>(0)(1,1)(1,1)(0,0)(1,1)(1,1)</math>
@@ 第187行： / 第189行： @@
 |<math>(0)(1,1)(1,1)(1,1)</math>
 |<math>\varepsilon_2</math>
+|<math>\psi(2)</math>
 |-
 |<math>(0)(1,1)(1,1)(1,1)(1,1)</math>
 |<math>\varepsilon_3</math>
+|<math>\psi(3)</math>
 |-
 |<math>(0)(1,1)(2,0)</math>
 |<math>\varepsilon_\omega</math>
+|<math>\psi(\omega)</math>
 |-
 |<math>(0)(1,1)(2,0)(1,0)</math>
@@ 第214行： / 第219行： @@
 |<math>(0)(1,1)(2,0)(1,0)(2,1)(3,0)(2,0)(3,1)(4,0)</math>
 |<math>\varepsilon_\omega^{\varepsilon_\omega}</math>
+|
 |-
 |<math>(0)(1,1)(2,0)(1,1)</math>
 |<math>\varepsilon_{\omega+1}</math>
+|<math>\psi(\omega+1)</math>
 |-
 |<math>(0)(1,1)(2,0)(1,1)(1,1)</math>
 |<math>\varepsilon_{\omega+2}</math>
+|<math>\psi (\omega +2)</math>
 |-
 |<math>(0)(1,1)(2,0)(1,1)(1,1)(1,1)</math>
 |<math>\varepsilon_{\omega+3}</math>
+|<math>\psi(\omega+3)</math>
 |-
 |<math>(0)(1,1)(2,0)(1,1)(2,0)</math>
 |<math>\varepsilon_{\omega\times2}</math>
+|<math>\psi (\omega \times 2)</math>
 |-
 |<math>(0)(1,1)(2,0)(1,1)(2,0)(1,1)(2,0)</math>
 |<math>\varepsilon_{\omega\times3}</math>
+|<math>\psi (\omega \times 3)</math>
 |-
 |<math>(0)(1,1)(2,0)(2,0)</math>
 |<math>\varepsilon_{\omega^2}</math>
+|<math>\psi (\omega ^2)</math>
 |-
 |<math>(0)(1,1)(2,0)(2,0)(2,0)</math>
 |<math>\varepsilon_{\omega^3}</math>
+|<math>\psi (\omega ^3)</math>
 |-
 |<math>(0)(1,1)(2,0)(3,0)</math>
 |<math>\varepsilon_{\omega^\omega}</math>
+|<math>\psi(\omega^\omega)</math>
 |-
 |<math>(0)(1,1)(2,0)(3,0)(4,0)</math>
 |<math>\varepsilon_{\omega^{\omega^\omega}}</math>
+|<math>\psi(\omega^{\omega^\omega})</math>
 |-
 |<math>(0)(1,1)(2,0)(3,1)</math>
 |<math>\varepsilon_{\varepsilon_0}</math>
+|<math>\psi(\psi(0))</math>
 |-
 |<math>(0)(1,1)(2,0)(3,1)(1,1)</math>
 |<math>\varepsilon_{\varepsilon_0+1}</math>
+|<math>\psi(\psi(0)+1)</math>
 |-
 |<math>(0)(1,1)(2,0)(3,1)(3,1)</math>
 |<math>\varepsilon_{\varepsilon_1}</math>
+|<math>\psi(\psi(1))</math>
 |-
 |<math>(0)(1,1)(2,0)(3,1)(4,0)</math>
 |<math>\varepsilon_{\varepsilon_\omega}</math>
+|<math>\psi(\psi(\omega))</math>
 |-
 |<math>(0)(1,1)(2,0)(3,1)(4,0)(5,1)</math>
 |<math>\varepsilon_{\varepsilon_{\varepsilon_0}}</math>
+|<math>\psi(\psi(\psi(0)))</math>
 |-
 |<math>(0)(1,1)(2,0)(3,1)(4,0)(5,1)(6,0)(7,1)</math>
 |<math>\varepsilon_{\varepsilon_{\varepsilon_{\varepsilon_0}}}</math>
+|<math>\psi(\psi(\psi(\psi(0))))</math>
 |-
 |<math>(0)(1,1)(2,1)</math>
 |<math>\zeta_0</math>
+|<math>\psi(\Omega)</math>
 |-
 |<math>(0)(1,1)(2,1)(1,0)(2,1)(3,1)</math>
@@ 第271行： / 第293行： @@
 |<math>(0)(1,1)(2,1)(1,1)</math>
 |<math>\varepsilon_{\zeta_0+1}</math>
+|<math>\psi(\Omega+1)</math>
 |-
 |<math>(0)(1,1)(2,1)(1,1)(1,0)(2,1)(3,1)(2,1)</math>
@@ 第277行： / 第300行： @@
 |<math>(0)(1,1)(2,1)(1,1)(1,1)</math>
 |<math>\varepsilon_{\zeta_0+2}</math>
+|
 |-
 |<math>(0)(1,1)(2,1)(1,1)(2,0)</math>