BHM分析：修订间差异

2025年7月27日 (日) 12:36的版本

本条目展示 BHM 的强度的列表分析。

Part 1

BHM	Veblen 函数
$(0)$	$1$
$(0) (0)$	$2$
$(0) (0) (0)$	$3$
$(0) (1)$	$ω$
$(0) (1) (0)$	$ω + 1$
$(0) (1) (0) (0)$	$ω + 2$
$(0) (1) (0) (0) (1)$	$ω \times 2$
$(0) (1) (0) (0) (1) (0)$	$ω \times 2 + 1$
$(0) (1) (0) (0) (1) (0) (0) (1)$	$ω \times 3$
$(0) (1) (0) (1)$	$ω^{2}$
$(0) (1) (0) (1) (0)$	$ω^{2} + 1$
$(0) (1) (0) (1) (0) (0) (1)$	$ω^{2} + ω$
$(0) (1) (0) (1) (0) (0) (1) (0) (0) (1)$	$ω^{2} + ω \times 2$
$(0) (1) (0) (1) (0) (0) (1) (0) (1)$	$ω^{2} \times 2$
$(0) (1) (0) (1) (0) (0) (1) (0) (1) (0) (0) (1)$	$ω^{2} \times 2 + ω$
$(0) (1) (0) (1) (0) (1)$	$ω^{3}$
$(0) (1) (1)$	$ω^{ω}$
$(0) (1) (1) (0)$	$ω^{ω} + 1$
$(0) (1) (1) (0) (0) (1)$	$ω^{ω} + ω$
$(0) (1) (1) (0) (0) (1) (0) (1)$	$ω^{ω} + ω \times 2$
$(0) (1) (1) (0) (0) (1) (1)$	$ω^{ω} \times 2$
$(0) (1) (1) (0) (1)$	$ω^{ω + 1}$
$(0) (1) (1) (0) (1) (0) (0) (1)$	$ω^{ω + 1} + ω$
$(0) (1) (1) (0) (1) (0) (0) (1) (1)$	$ω^{ω + 1} + ω^{ω}$
$(0) (1) (1) (0) (1) (0) (0) (1) (1) (0) (1)$	$ω^{ω + 1} \times 2$
$(0) (1) (1) (0) (1) (0) (1)$	$ω^{ω + 2}$
$(0) (1) (1) (0) (1) (0) (1) (1)$	$ω^{ω \times 2}$
$(0) (1) (1) (0) (1) (0) (1) (1) (0) (1)$	$ω^{ω \times 2 + 1}$
$(0) (1) (1) (0) (1) (0) (1) (1) (0) (1) (0) (1) (1)$	$ω^{ω \times 3}$
$(0) (1) (1) (0) (1) (1)$	$ω^{ω^{2}}$
$(0) (1) (1) (0) (1) (1) (0) (1) (0) (1) (1)$	$ω^{ω^{2} + ω}$
$(0) (1) (1) (0) (1) (1) (0) (1) (0) (1) (1)$	$ω^{ω^{2} \times 2}$
$(0) (1) (1) (0) (1) (1) (0) (1) (1)$	$ω^{ω^{3}}$
$(0) (1) (1) (1)$	$ω^{ω^{ω}}$
$(0) (1) (1) (1) (0) (1) (1)$	$ω^{ω^{ω + 1}}$
$(0) (1) (1) (1) (0) (1) (1) (0) (1) (1) (1)$	$ω^{ω^{ω \times 2}}$
$(0) (1) (1) (1) (0) (1) (1) (1)$	$ω^{ω^{ω^{2}}}$
$(0) (1) (1) (1) (1)$	$ω^{ω^{ω^{ω}}}$
$(0) (1) (2)$	$ε_{0}$

Part 2

BHM	Veblen 函数
$(0) (1) (2) (0) (0) (1)$	$ε_{0} + ω$
$(0) (1) (2) (0) (0) (1) (1)$	$ε_{0} + ω^{2}$
$(0) (1) (2) (0) (0) (1) (2)$	$ε_{0} \times 2$
$(0) (1) (2) (0) (1)$	$ε_{0} \times ω$
$(0) (1) (2) (0) (1) (0) (1) (1)$	$ε_{0} \times ω^{ω}$
$(0) (1) (2) (0) (1) (0) (1) (2)$	$ε_{0}^{2}$
$(0) (1) (2) (0) (1) (0) (1) (2) (0) (1) (0) (1) (2)$	$ε_{0}^{3}$
$(0) (1) (2) (0) (1) (1)$	$ε_{0}^{ω}$
$(0) (1) (2) (0) (1) (1) (0) (1) (0) (1) (2)$	$ε_{0}^{ω + 1}$
$(0) (1) (2) (0) (1) (1) (0) (1) (0) (1) (2) (0) (1) (1)$	$ε_{0}^{ω \times 2}$
$(0) (1) (2) (0) (1) (1) (0) (1) (1)$	$ε_{0}^{ω^{2}}$
$(0) (1) (2) (0) (1) (1) (0) (1) (1) (1)$	$ε_{0}^{ω^{ω}}$
$(0) (1) (2) (0) (1) (1) (0) (1) (2)$	$ε_{0}^{ε_{0}}$
$(0) (1) (2) (0) (1) (1) (1)$	$ε_{0}^{ε_{0} \times ω}$
$(0) (1) (2) (0) (1) (1) (1) (0) (1) (2)$	$ε_{0}^{ε_{0}^{2}}$
$(0) (1) (2) (0) (1) (1) (1) (1)$	$ε_{0}^{ε_{0}^{ω}}$
$(0) (1) (2) (0) (1) (1) (1) (1) (0) (1) (2)$	$ε_{0}^{ε_{0}^{ε_{0}}}$
$(0) (1) (2) (0) (1) (2)$	$ε_{1}$
$(0) (1) (2) (0) (1) (2) (0) (1)$	$ε_{1} \times ω$
$(0) (1) (2) (0) (1) (2) (0) (1) (0) (1) (2)$	$ε_{1} \times ε_{0}$
$(0) (1) (2) (0) (1) (2) (0) (1) (0) (1) (2) (0) (1) (1) (0) (1) (2)$	$ε_{1} \times ε_{0}^{ε_{0}}$
$(0) (1) (2) (0) (1) (2) (0) (1) (0) (1) (2) (0) (1) (2)$	$ε_{1}^{2}$
$(0) (1) (2) (0) (1) (2) (0) (1) (1)$	$ε_{1}^{ω}$
$(0) (1) (2) (0) (1) (2) (0) (1) (1) (0) (1) (2)$	$ε_{1}^{ε_{0}}$
$(0) (1) (2) (0) (1) (2) (0) (1) (1) (0) (1) (2) (0) (1) (2)$	$ε_{1}^{ε_{1}}$
$(0) (1) (2) (0) (1) (2) (0) (1) (2)$	$ε_{2}$
$(0) (1) (2) (1)$	$ε_{ω}$
$(0) (1) (2) (1) (0) (1) (2)$	$ε_{ω + 1}$
$(0) (1) (2) (1) (0) (1) (2) (0) (1) (2) (1)$	$ε_{ω \times 2}$
$(0) (1) (2) (1) (0) (1) (2) (1)$	$ε_{ω^{2}}$
$(0) (1) (2) (1) (1)$	$ε_{ω^{ω}}$
$(0) (1) (2) (1) (1) (2)$	$ε_{ε_{0}}$
$(0) (1) (2) (1) (1) (2) (0) (1) (2) (1)$	$ε_{ε_{0} \times ω}$
$(0) (1) (2) (1) (1) (2) (0) (1) (2) (1) (0) (1) (2) (1) (1) (2)$	$ε_{ε_{0}^{2}}$
$(0) (1) (2) (1) (1) (2) (0) (1) (2) (1) (1)$	$ε_{ε_{0}^{ω}}$
$(0) (1) (2) (1) (1) (2) (0) (1) (2) (1) (1) (0) (1) (2) (1) (1) (2)$	$ε_{ε_{0}^{ε_{0}}}$
$(0) (1) (2) (1) (1) (2) (0) (1) (2) (1) (1) (2)$	$ε_{ε_{1}}$
$(0) (1) (2) (1) (1) (2) (1)$	$ε_{ε_{ω}}$
$(0) (1) (2) (1) (1) (2) (1) (1) (2)$	$ε_{ε_{ε_{0}}}$
$(0) (1) (2) (1) (2)$	$ζ_{0}$
$(0) (1) (2) (1) (2)$	$ζ_{0}$
$(0) (1) (2) (1) (2) (0) (1) (0) (1) (2) (1) (2)$	$ζ_{0}^{2}$
$(0) (1) (2) (1) (2) (0) (1) (1)$	$ζ_{0}^{ω}$
$(0) (1) (2) (1) (2) (0) (1) (1) (0) (1) (2) (1) (2)$	$ζ_{0}^{ζ_{0}}$
$(0) (1) (2) (1) (2) (0) (1) (2)$	$ε_{ζ_{0} + 1}$
$(0) (1) (2) (1) (2) (0) (1) (2)$	$ε_{ζ_{0} + 1}$
$(0) (1) (2) (1) (2) (0) (1) (2) (0) (1) (2) (1) (1) (2)$	$ε_{ζ_{0} + ε_{0}}$
$(0) (1) (2) (1) (2) (0) (1) (2) (1)$	$ε_{ζ_{0} \times ω}$
$(0) (1) (2) (1) (2) (0) (1) (2) (1) (0) (1) (2) (1) (2)$	$ε_{ζ_{0}^{2}}$
$(0) (1) (2) (1) (2) (0) (1) (2) (1) (1) (0) (1) (2) (1) (2)$	$ε_{ζ_{0}^{ζ_{0}}}$
$(0) (1) (2) (1) (2) (0) (1) (2) (1) (1) (2)$	$ε_{ε_{ζ_{0} + 1}}$
$(0) (1) (2) (1) (2) (0) (1) (2) (1) (2)$	$ζ_{1}$
$(0) (1) (2) (1) (2) (1)$	$ζ_{ω}$
$(0) (1) (2) (1) (2) (1) (1) (2)$	$ζ_{ε_{0}}$
$(0) (1) (2) (1) (2) (1) (1) (2) (1) (2)$	$ζ_{ζ_{0}}$
$(0) (1) (2) (1) (2) (1) (2)$	$η_{0}$
$(0) (1) (2) (1) (2) (1) (2) (0) (1) (2)$	$ε_{η_{0} + 1}$
$(0) (1) (2) (1) (2) (1) (2) (0) (1) (2) (1) (2)$	$ζ_{η_{0} + 1}$
$(0) (1) (2) (1) (2) (1) (2) (0) (1) (2) (1) (2) (1) (2)$	$η_{1}$
$(0) (1) (2) (1) (2) (1) (2) (1)$	$η_{ω}$
$(0) (1) (2) (1) (2) (1) (2) (1) (1) (2) (1) (2) (1) (2)$	$η_{η_{0}}$
$(0) (1) (2) (1) (2) (1) (2) (1) (2)$	$φ (4, 0)$
$(0) (1) (2) (2)$	$φ (ω, 0)$
$(0) (1) (2) (2) (0) (1) (2)$	$φ (1, φ (ω, 0) + 1)$
$(0) (1) (2) (2) (0) (1) (2) (2)$	$φ (ω, 1)$
$(0) (1) (2) (2) (1)$	$φ (ω, ω)$
$(0) (1) (2) (2) (1) (1) (2)$	$φ (ω, ε_{0})$
$(0) (1) (2) (2) (1) (1) (2) (1) (2) (2)$	$φ (ω, φ (ω, 0))$
$(0) (1) (2) (2) (1) (2)$	$φ (ω + 1, 0)$
$(0) (1) (2) (2) (1) (2) (1) (2) (2)$	$φ (ω \times 2, 0)$
$(0) (1) (2) (2) (1) (2) (2)$	$φ (ω^{2}, 0)$
$(0) (1) (2) (2) (2)$	$φ (ω^{ω}, 0)$
$(0) (1) (2) (3)$	$φ (ε_{0}, 0)$
$(0) (1) (2) (3) (1) (2) (3)$	$φ (ε_{1}, 0)$
$(0) (1) (2) (3) (2) (3)$	$φ (ζ_{0}, 0)$
$(0) (1) (2) (3) (3)$	$φ (φ (ω, 0), 0)$
$(0) (1) (2) (3) (4)$	$φ (φ (ε_{0}, 0), 0)$
$(0, 0) (1, 1)$	$φ (1, 0, 0)$

Part 3

BHM	Veblen 函数
$(0, 0) (1, 1) (0, 0)$	$φ (1, 0, 0) + 1$
$(0, 0) (1, 1) (0, 0) (0, 0) (1, 1)$	$φ (1, 0, 0) \times 2$
$(0, 0) (1, 1) (0, 0) (1, 0)$	$ω^{φ (1, 0, 0) + 1}$
$(0, 0) (1, 1) (0, 0) (1, 0) (1, 0)$	$ω^{ω^{φ (1, 0, 0) + 1}}$
$(0, 0) (1, 1) (0, 0) (1, 0) (2, 0)$	$φ (1, φ (1, 0, 0) + 1)$
$(0, 0) (1, 1) (0, 0) (1, 0) (2, 0) (0, 0) (1, 1)$	$φ (1, φ (1, 0, 0) \times 2)$
$(0, 0) (1, 1) (0, 0) (1, 0) (2, 0) (1, 0) (1, 0) (2, 0)$	$φ (1, φ (1, φ (1, 0, 0) + 1))$
$(0, 0) (1, 1) (0, 0) (1, 0) (2, 0) (1, 0) (2, 0)$	$φ (2, φ (1, 0, 0) + 1)$
$(0, 0) (1, 1) (0, 0) (1, 0) (2, 0) (2, 0)$	$φ (ω, φ (1, 0, 0) + 1)$
$(0, 0) (1, 1) (0, 0) (1, 0) (2, 0) (2, 0) (1, 0) (2, 0)$	$φ (ω + 1, φ (1, 0, 0) + 1)$
$(0, 0) (1, 1) (0, 0) (1, 0) (2, 0) (2, 0) (1, 0) (2, 0) (2, 0)$	$φ (ω^{2}, φ (1, 0, 0) + 1)$
$(0, 0) (1, 1) (0, 0) (1, 0) (2, 0) (2, 0) (2, 0)$	$φ (ω^{ω}, φ (1, 0, 0) + 1)$
$(0, 0) (1, 1) (0, 0) (1, 0) (2, 0) (3, 0)$	$φ (φ (1, 0), φ (1, 0, 0) + 1)$
$(0, 0) (1, 1) (0, 0) (1, 0) (2, 0) (3, 0) (4, 0)$	$φ (φ (φ (1, 0), 0), φ (1, 0, 0) + 1)$
$(0, 0) (1, 1) (0, 0) (1, 0) (2, 0) (3, 0) (4, 0) (5, 0)$	$φ (φ (φ (φ (1, 0), 0), 0), φ (1, 0, 0) + 1)$
$(0, 0) (1, 1) (0, 0) (1, 1)$	$φ (φ (1, 0, 0), 1)$
$(0, 0) (1, 1) (0, 0) (1, 1) (0, 0) (1, 1)$	$φ (φ (1, 0, 0), 2)$
$(0, 0) (1, 1) (1, 0)$	$φ (φ (1, 0, 0), ω)$
$(0, 0) (1, 1) (1, 0) (0, 0) (1, 1)$	$φ (φ (1, 0, 0), ω + 1)$
$(0, 0) (1, 1) (1, 0) (0, 0) (1, 1) (0, 0) (1, 1) (1, 0)$	$φ (φ (1, 0, 0), ω \times 2)$
$(0, 0) (1, 1) (1, 0) (0, 0) (1, 1) (1, 0)$	$φ (φ (1, 0, 0), ω^{2})$
$(0, 0) (1, 1) (1, 0) (1, 0)$	$φ (φ (1, 0, 0), ω^{ω})$
$(0, 0) (1, 1) (1, 0) (1, 0) (1, 0)$	$φ (φ (1, 0, 0), ω^{ω^{ω}})$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0)$	$φ (φ (1, 0, 0), φ (1, 0))$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (1, 0) (2, 0)$	$φ (φ (1, 0, 0), φ (2, 0))$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (2, 0)$	$φ (φ (1, 0, 0), φ (ω, 0))$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 0)$	$φ (φ (1, 0, 0), φ (φ (1, 0), 0))$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 0) (4, 0)$	$φ (φ (1, 0, 0), φ (φ (φ (1, 0), 0), 0))$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1)$	$φ (φ (1, 0, 0), φ (1, 0, 0))$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (0, 0) (1, 1)$	$φ (φ (1, 0, 0), φ (1, 0, 0) + 1)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (0, 0) (1, 1) (0, 0) (1, 1)$	$φ (φ (1, 0, 0), φ (1, 0, 0) + 2)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (0, 0) (1, 1) (0, 0) (1, 1) (1, 0)$	$φ (φ (1, 0, 0), φ (1, 0, 0) + ω)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (0, 0) (1, 1) (0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1)$	$φ (φ (1, 0, 0), φ (1, 0, 0) \times 2)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (0, 0) (1, 1) (1, 0)$	$φ (φ (1, 0, 0), ω^{φ (1, 0, 0) + 1})$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (0, 0) (1, 1) (1, 0) (1, 0) (2, 0)$	$φ (φ (1, 0, 0), φ (1, φ (1, 0, 0) + 1))$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (1, 0) (2, 0)$	$φ (φ (1, 0, 0), φ (2, φ (1, 0, 0) + 1))$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (2, 0)$	$φ (φ (1, 0, 0), φ (ω, φ (1, 0, 0) + 1))$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 0)$	$φ (φ (1, 0, 0), φ (φ (1, 0), φ (1, 0, 0) + 1))$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1)$	$φ (φ (1, 0, 0), φ (φ (1, 0, 0), 1))$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0)$	$φ (φ (1, 0, 0), φ (φ (1, 0, 0), ω))$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0) (0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1)$	$φ (φ (1, 0, 0), φ (φ (1, 0, 0), ω + 1))$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0) (1, 0)$	$φ (φ (1, 0, 0), φ (φ (1, 0, 0), ω^{ω}))$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0) (1, 0) (2, 0)$	$φ (φ (1, 0, 0), φ (φ (1, 0, 0), φ (1, 0)))$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0) (1, 0) (2, 0) (2, 0)$	$φ (φ (1, 0, 0), φ (φ (1, 0, 0), φ (ω, 0)))$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0) (1, 0) (2, 0) (3, 1)$	$φ (φ (1, 0, 0), φ (φ (1, 0, 0), φ (1, 0, 0)))$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0) (1, 0) (2, 0) (3, 1) (0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0) (1, 0) (2, 0) (3, 1)$	$φ (φ (1, 0, 0), φ (φ (1, 0, 0), φ (φ (1, 0, 0), 1)))$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0) (2, 0)$	$φ (φ (1, 0, 0) + 1, 0)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0) (2, 0) (0, 0) (1, 1)$	$φ (φ (1, 0, 0), φ (φ (1, 0, 0) + 1, 0) + 1)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0) (2, 0) (0, 0) (1, 1) (0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0) (2, 0)$	$φ (φ (1, 0, 0), φ (φ (1, 0, 0) + 1, 0) \times 2)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0) (2, 0) (0, 0) (1, 1) (1, 0)$	$φ (φ (1, 0, 0), ω^{φ (φ (1, 0, 0) + 1, 0) + 1})$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0) (2, 0) (0, 0) (1, 1) (1, 0) (1, 0) (2, 0)$	$φ (φ (1, 0, 0), φ (1, φ (φ (1, 0, 0) + 1, 0) + 1))$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0) (2, 0) (0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1)$	$φ (φ (1, 0, 0), φ (φ (1, 0, 0), φ (φ (1, 0, 0) + 1, 0) + 1))$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0) (2, 0) (0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0) (2, 0)$	$φ (φ (1, 0, 0), φ (φ (1, 0, 0), φ (φ (1, 0, 0) + 1, 0) \times 2))$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0) (2, 0) (0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0) (1, 0) (2, 0)$	$φ (φ (1, 0, 0), φ (φ (1, 0, 0), φ (1, φ (φ (1, 0, 0) + 1, 0) + 1)))$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0) (2, 0) (0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0) (1, 0) (2, 0) (3, 1)$	$φ (φ (1, 0, 0), φ (φ (1, 0, 0), φ (φ (1, 0, 0), φ (φ (1, 0, 0) + 1, 0) + 1)))$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0) (2, 0) (0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0) (2, 0)$	$φ (φ (1, 0, 0) + 1, 1)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0) (2, 0) (1, 0)$	$φ (φ (1, 0, 0) + 1, ω)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0) (2, 0) (1, 0) (1, 0) (2, 0)$	$φ (φ (1, 0, 0) + 1, φ (1, 0))$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0) (2, 0) (1, 0) (1, 0) (2, 0) (3, 1)$	$φ (φ (1, 0, 0) + 1, φ (1, 0, 0))$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0) (2, 0) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0) (2, 0)$	$φ (φ (1, 0, 0) + 1, φ (φ (1, 0, 0) + 1, 0))$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0) (2, 0) (1, 0) (2, 0)$	$φ (φ (1, 0, 0) + 2, 0)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0) (2, 0) (1, 0) (2, 0) (2, 0)$	$φ (φ (1, 0, 0) + ω, 0)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0) (2, 0) (1, 0) (2, 0) (3, 0)$	$φ (φ (1, 0, 0) + φ (1, 0), 0)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0) (2, 0) (1, 0) (2, 0) (3, 1)$	$φ (φ (1, 0, 0) \times 2, 0)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0) (2, 0) (1, 0) (2, 0) (3, 1) (1, 0) (2, 0) (1, 0) (2, 0) (3, 1)$	$φ (φ (1, 0, 0) \times 3, 0)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0) (2, 0) (2, 0)$	$φ (ω^{φ (1, 0, 0) + 1}, 0)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0) (2, 0) (3, 0)$	$φ (φ (1, φ (1, 0, 0) + 1), 0)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0) (2, 0) (3, 1)$	$φ (φ (φ (1, 0, 0), 1), 0)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0) (2, 0) (3, 1) (1, 0) (2, 0)$	$φ (φ (φ (1, 0, 0), 1) + 1, 0)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0) (2, 0) (3, 1) (1, 0) (2, 0) (2, 0)$	$φ (ω^{φ (φ (1, 0, 0), 1) + 1}, 0)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0) (2, 0) (3, 1) (1, 0) (2, 0) (3, 0)$	$φ (φ (1, φ (φ (1, 0, 0), 1) + 1), 0)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0) (2, 0) (3, 1) (1, 0) (2, 0) (3, 1)$	$φ (φ (φ (1, 0, 0), 2), 0)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (2, 0)$	$φ (φ (φ (1, 0, 0), ω), 0)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (2, 0) (1, 0) (2, 0) (3, 1)$	$φ (φ (φ (1, 0, 0), ω + 1), 0)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (2, 0) (1, 0) (2, 0) (3, 1) (1, 0) (2, 0) (3, 1) (2, 0)$	$φ (φ (φ (1, 0, 0), ω \times 2), 0)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (2, 0) (2, 0)$	$φ (φ (φ (1, 0, 0), ω^{ω}), 0)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (2, 0) (2, 0) (3, 0)$	$φ (φ (φ (1, 0, 0), φ (1, 0)), 0)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (2, 0) (2, 0) (3, 1)$	$φ (φ (φ (1, 0, 0), φ (1, 0, 0)), 0)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (2, 0) (2, 0) (3, 1) (1, 0) (2, 0) (3, 1)$	$φ (φ (φ (1, 0, 0), φ (1, 0, 0) + 1), 0)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (2, 0) (2, 0) (3, 1) (1, 0) (2, 0) (3, 1) (2, 0)$	$φ (φ (φ (1, 0, 0), ω^{φ (1, 0, 0) + 1}), 0)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (2, 0) (2, 0) (3, 1) (1, 0) (2, 0) (3, 1) (2, 0) (2, 0) (3, 0)$	$φ (φ (φ (1, 0, 0), φ (1, φ (1, 0, 0) + 1)), 0)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (2, 0) (2, 0) (3, 1) (1, 0) (2, 0) (3, 1) (2, 0) (2, 0) (3, 1)$	$φ (φ (φ (1, 0, 0), φ (φ (1, 0, 0), 1)), 0)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (2, 0) (2, 0) (3, 1) (2, 0)$	$φ (φ (φ (1, 0, 0), φ (φ (1, 0, 0), ω)), 0)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (2, 0) (2, 0) (3, 1) (2, 0) (2, 0) (3, 1)$	$φ (φ (φ (1, 0, 0), φ (φ (1, 0, 0), φ (1, 0, 0))), 0)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (2, 0) (3, 0)$	$φ (φ (φ (1, 0, 0) + 1, 0), 0)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (2, 0) (3, 0) (2, 0) (3, 0)$	$φ (φ (φ (1, 0, 0) + 2, 0), 0)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (2, 0) (3, 0) (2, 0) (3, 1)$	$φ (φ (φ (1, 0, 0) \times 2, 0), 0)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (2, 0) (3, 0) (3, 0)$	$φ (φ (ω^{φ (1, 0, 0) + 1}, 0), 0)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (2, 0) (3, 1)$	$φ (φ (φ (φ (1, 0, 0), 1), 0), 0)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (3, 0)$	$φ (φ (φ (φ (1, 0, 0), ω), 0), 0)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (3, 0) (3, 0) (4, 0)$	$φ (φ (φ (φ (1, 0, 0), φ (1, 0)), 0), 0)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (3, 0) (3, 0) (4, 0) (5, 1)$	$φ (φ (φ (φ (1, 0, 0), φ (1, 0, 0)), 0), 0)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (3, 0) (3, 0) (4, 0) (5, 1) (2, 0) (3, 1)$	$φ (φ (φ (φ (1, 0, 0), φ (1, 0, 0) + 1), 0), 0)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (3, 0) (3, 0) (4, 0) (5, 1) (2, 0) (3, 1) (3, 0) (3, 0) (4, 0) (5, 1)$	$φ (φ (φ (φ (1, 0, 0), φ (φ (1, 0, 0), 1)), 0), 0)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (3, 0) (3, 0) (4, 0) (5, 1) (3, 0)$	$φ (φ (φ (φ (1, 0, 0), φ (φ (1, 0, 0), ω)), 0), 0)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (3, 0) (3, 0) (4, 0) (5, 1) (3, 0) (4, 0)$	$φ (φ (φ (φ (1, 0, 0) + 1, 0), 0), 0)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (3, 0) (3, 0) (4, 0) (5, 1) (3, 0) (4, 0) (5, 0)$	$φ (φ (φ (φ (1, φ (1, 0, 0) + 1), 0), 0), 0)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (3, 0) (3, 0) (4, 0) (5, 1) (3, 0) (4, 0) (5, 1)$	$φ (φ (φ (φ (φ (1, 0, 0), 1), 0), 0), 0)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (3, 0) (3, 0) (4, 0) (5, 1) (4, 0) (5, 1)$	$φ (φ (φ (φ (φ (φ (1, 0, 0), 1), 0), 0), 0), 0)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 1)$	$φ (1, 0, 1)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 1) (0, 0) (1, 1)$	$φ (φ (1, 0, 0), φ (1, 0, 1) + 1)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 1) (0, 0) (1, 1) (1, 0)$	$φ (φ (1, 0, 0), ω^{φ (1, 0, 1) + 1})$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 1) (0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1)$	$φ (φ (1, 0, 0), φ (φ (1, 0, 0), φ (1, 0, 1) + 1))$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 1) (0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1)$	$φ (φ (1, 0, 0), φ (φ (1, 0, 0), φ (1, 0, 1) + 2))$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 1) (0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (2, 0)$	$φ (φ (1, 0, 0), φ (φ (1, 0, 0), φ (1, 0, 1) + ω))$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 1) (0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (0, 0) (1, 1) (1, 0) (1, 0) (2, 1)$	$φ (φ (1, 0, 0), φ (φ (1, 0, 0), φ (1, 0, 1) \times 2))$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 1) (0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0)$	$φ (φ (1, 0, 0), φ (φ (1, 0, 0), ω^{φ (1, 0, 1) + 1}))$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 1) (0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0) (1, 0) (2, 1) (3, 1)$	$φ (φ (1, 0, 0), φ (φ (1, 0, 0), φ (φ (1, 0, 0), φ (1, 0, 1) + 1)))$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 1) (0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0) (2, 0)$	$φ (φ (1, 0, 0) + 1, φ (1, 0, 1) + 1)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 1) (0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0) (2, 0) (1, 0) (2, 0) (3, 1)$	$φ (φ (1, 0, 0) \times 2, φ (1, 0, 1) + 1)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 1) (0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0) (2, 0) (3, 1)$	$φ (φ (φ (1, 0, 0), 1), φ (1, 0, 1) + 1)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 1) (0, 0) (1, 1) (1, 0) (1, 0) (2, 0) (3, 1) (2, 0) (3, 1)$	$φ (φ (φ (φ (1, 0, 0), 1), 0), φ (1, 0, 1) + 1)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 1) (0, 0) (1, 1) (1, 0) (1, 0) (2, 1)$	$φ (φ (1, 0, 1), 1)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 1) (1, 0)$	$φ (φ (1, 0, 1), ω)$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 1) (1, 0) (1, 0) (2, 0)$	$φ (φ (1, 0, 1), φ (1, 0))$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 1) (1, 0) (1, 0) (2, 0) (3, 1)$	$φ (φ (1, 0, 1), φ (1, 0, 0))$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 1) (1, 0) (1, 0) (2, 0) (3, 1) (0, 0) (1, 1) (1, 0) (1, 0) (2, 1) (1, 0) (1, 0) (2, 0) (3, 1)$	$φ (φ (1, 0, 1), φ (φ (1, 0, 0), 1))$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0)$	$φ (φ (1, 0, 1), φ (φ (1, 0, 0), ω))$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0) (1, 0) (2, 0) (3, 1)$	$φ (φ (1, 0, 1), φ (φ (1, 0, 0), φ (1, 0, 0)))$
$(0, 0) (1, 1) (1, 0) (1, 0) (2, 1) (1, 0) (1, 0) (2, 0) (3, 1) (1, 0) (2, 0)$	$φ (φ (1, 0, 1), φ (φ (1, 0, 0) + 1, 0))$

@@ 第1行： / 第1行： @@
-本条目展示[[BHM]]的强度的列表分析
+本条目展示 [[BHM]] 的强度的列表分析。
-=== 1. ===
+=== Part 1 ===
 {| class="wikitable"
-|+
 !BHM
-!veblen函数
+!Veblen 函数
 !
 !
@@ 第11行： / 第10行： @@
 |<math>(0)</math>
 |<math>1</math>
-|
-|
 |-
 |<math>(0)(0)</math>
 |<math>2</math>
-|
-|
 |-
 |<math>(0)(0)(0)</math>
 |<math>3</math>
-|
-|
 |-
 |<math>(0)(1)</math>
 |<math>\omega</math>
-|
-|
 |-
 |<math>(0)(1)(0)</math>
 |<math>\omega +1</math>
-|
-|
 |-
 |<math>(0)(1)(0)(0)</math>
 |<math>\omega +2</math>
-|
-|
 |-
 |<math>(0)(1)(0)(0)(1)</math>
 |<math>\omega \times 2</math>
-|
-|
 |-
 |<math>(0)(1)(0)(0)(1)(0)</math>
 |<math>\omega \times 2 +1</math>
-|
-|
 |-
 |<math>(0)(1)(0)(0)(1)(0)(0)(1)</math>
 |<math>\omega \times 3</math>
-|
-|
 |-
 |<math>(0)(1)(0)(1)</math>
 |<math>\omega ^2</math>
-|
-|
 |-
 |<math>(0)(1)(0)(1)(0)</math>
 |<math>\omega ^2+1</math>
-|
-|
 |-
 |<math>(0)(1)(0)(1)(0)(0)(1)</math>
 |<math>\omega ^2+\omega</math>
-|
-|
 |-
 |<math>(0)(1)(0)(1)(0)(0)(1)(0)(0)(1)</math>
 |<math>\omega ^2+\omega\times 2</math>
-|
-|
 |-
 |<math>(0)(1)(0)(1)(0)(0)(1)(0)(1)</math>
 |<math>\omega ^2\times 2</math>
-|
-|
 |-
 |<math>(0)(1)(0)(1)(0)(0)(1)(0)(1)(0)(0)(1)</math>
 |<math>\omega ^2\times 2 + \omega</math>
-|
-|
 |-
 |<math>(0)(1)(0)(1)(0)(1)</math>
 |<math>\omega ^3</math>
-|
-|
 |-
 |<math>(0)(1)(1)</math>
 |<math>\omega ^\omega</math>
-|
-|
 |-
 |<math>(0)(1)(1)(0)</math>
 |<math>\omega ^\omega+1</math>
-|
-|
 |-
 |<math>(0)(1)(1)(0)(0)(1)</math>
 |<math>\omega ^\omega+\omega</math>
-|
-|
 |-
 |<math>(0)(1)(1)(0)(0)(1)(0)(1)</math>
 |<math>\omega ^\omega+\omega\times 2</math>
-|
-|
 |-
 |<math>(0)(1)(1)(0)(0)(1)(1)</math>
 |<math>\omega ^\omega \times 2</math>
-|
-|
 |-
 |<math>(0)(1)(1)(0)(1)</math>
 |<math>\omega ^{\omega +1}</math>
-|
-|
 |-
 |<math>(0)(1)(1)(0)(1)(0)(0)(1)</math>
 |<math>\omega ^{\omega +1}+\omega</math>
-|
-|
 |-
 |<math>(0)(1)(1)(0)(1)(0)(0)(1)(1)</math>
 |<math>\omega ^{\omega +1}+\omega^{\omega}</math>
-|
-|
 |-
 |<math>(0)(1)(1)(0)(1)(0)(0)(1)(1)(0)(1)</math>
 |<math>\omega ^{\omega +1}\times 2</math>
-|
-|
 |-
 |<math>(0)(1)(1)(0)(1)(0)(1)</math>
 |<math>\omega ^{\omega +2}</math>
-|
-|
 |-
 |<math>(0)(1)(1)(0)(1)(0)(1)(1)</math>
 |<math>\omega ^{\omega \times 2}</math>
-|
-|
 |-
 |<math>(0)(1)(1)(0)(1)(0)(1)(1)(0)(1)</math>
 |<math>\omega ^{\omega \times 2+1}</math>
-|
-|
 |-
 |<math>(0)(1)(1)(0)(1)(0)(1)(1)(0)(1)(0)(1)(1)</math>
 |<math>\omega ^{\omega \times 3}</math>
-|
-|
 |-
 |<math>(0)(1)(1)(0)(1)(1)</math>
 |<math>\omega ^{\omega ^2}</math>
-|
-|
 |-
 |<math>(0)(1)(1)(0)(1)(1)(0)(1)(0)(1)(1)</math>
 |<math>\omega ^{\omega ^2+\omega}</math>
-|
-|
 |-
 |<math>(0)(1)(1)(0)(1)(1)(0)(1)(0)(1)(1)</math>
 |<math>\omega ^{\omega ^2\times 2}</math>
-|
-|
 |-
 |<math>(0)(1)(1)(0)(1)(1)(0)(1)(1)</math>
 |<math>\omega ^{\omega ^3}</math>
-|
-|
 |-
 |<math>(0)(1)(1)(1)</math>
 |<math>\omega ^{\omega ^\omega}</math>
-|
-|
 |-
 |<math>(0)(1)(1)(1)(0)(1)(1)</math>
 |<math>\omega ^{\omega ^{\omega+1}}</math>
-|
-|
 |-
 |<math>(0)(1)(1)(1)(0)(1)(1)(0)(1)(1)(1)</math>
 |<math>\omega ^{\omega ^{\omega\times 2}}</math>
-|
-|
 |-
 |<math>(0)(1)(1)(1)(0)(1)(1)(1)</math>
 |<math>\omega ^{\omega ^{\omega^2}}</math>
-|
-|
 |-
 |<math>(0)(1)(1)(1)(1)</math>
 |<math>\omega ^{\omega ^{\omega^\omega}}</math>
-|
-|
 |-
 |<math>(0)(1)(2)</math>
 |<math>\varepsilon_0</math>
-|
-|
 |}
-=== 2. ===
+=== Part 2 ===
 {| class="wikitable"
-|+
 !BHM
-!veblen函数
+!Veblen 函数
 !
 !
@@ 第215行： / 第135行： @@
 |<math>(0)(1)(2)(0)(0)(1)</math>
 |<math>\varepsilon_0 + \omega</math>
-|
-|
 |-
 |<math>(0)(1)(2)(0)(0)(1)(1)</math>
 |<math>\varepsilon_0 +\omega^2</math>
-|
-|
 |-
 |<math>(0)(1)(2)(0)(0)(1)(2)</math>
 |<math>\varepsilon_0 \times 2</math>
-|
-|
 |-
 |<math>(0)(1)(2)(0)(1)</math>
 |<math>\varepsilon_0 \times \omega</math>
-|
-|
 |-
 |<math>(0)(1)(2)(0)(1)(0)(1)(1)</math>
 |<math>\varepsilon_0 \times \omega^\omega</math>
-|
-|
 |-
 |<math>(0)(1)(2)(0)(1)(0)(1)(2)</math>
 |<math>\varepsilon_0 ^2</math>
-|
-|
 |-
 |<math>(0)(1)(2)(0)(1)(0)(1)(2)(0)(1)(0)(1)(2)</math>
 |<math>\varepsilon_0 ^3</math>
-|
-|
 |-
 |<math>(0)(1)(2)(0)(1)(1)</math>
 |<math>\varepsilon_0 ^\omega</math>
-|
-|
 |-
 |<math>(0)(1)(2)(0)(1)(1)(0)(1)(0)(1)(2)</math>
 |<math>\varepsilon_0 ^{\omega+1}</math>
-|
-|
 |-
 |<math>(0)(1)(2)(0)(1)(1)(0)(1)(0)(1)(2)(0)(1)(1)</math>
 |<math>\varepsilon_0 ^{\omega\times 2}</math>
-|
-|
 |-
 |<math>(0)(1)(2)(0)(1)(1)(0)(1)(1)</math>
 |<math>\varepsilon_0 ^{\omega^2}</math>
-|
-|
 |-
 |<math>(0)(1)(2)(0)(1)(1)(0)(1)(1)(1)</math>
 |<math>\varepsilon_0 ^{\omega^\omega}</math>
-|
-|
 |-
 |<math>(0)(1)(2)(0)(1)(1)(0)(1)(2)</math>
 |<math>\varepsilon_0 ^{\varepsilon_0}</math>
-|
-|
 |-
 |<math>(0)(1)(2)(0)(1)(1)(1)</math>
 |<math>\varepsilon_0 ^{\varepsilon_0\times \omega}</math>
-|
-|
 |-
 |<math>(0)(1)(2)(0)(1)(1)(1)(0)(1)(2)</math>
 |<math>\varepsilon_0 ^{\varepsilon_0^2}</math>
-|
-|
 |-
 |<math>(0)(1)(2)(0)(1)(1)(1)(1)</math>
 |<math>\varepsilon_0 ^{\varepsilon_0^\omega}</math>
-|
-|
 |-
 |<math>(0)(1)(2)(0)(1)(1)(1)(1)(0)(1)(2)</math>
 |<math>\varepsilon_0 ^{\varepsilon_0^{\varepsilon_0}}</math>
-|
-|
 |-
 |<math>(0)(1)(2)(0)(1)(2)</math>
 |<math>\varepsilon_1 </math>
-|
-|
 |-
 |<math>(0)(1)(2)(0)(1)(2)(0)(1)</math>
 |<math>\varepsilon_1 \times \omega</math>
-|
-|
 |-
 |<math>(0)(1)(2)(0)(1)(2)(0)(1)(0)(1)(2)</math>
 |<math>\varepsilon_1 \times \varepsilon_0</math>
-|
-|
 |-
 |<math>(0)(1)(2)(0)(1)(2)(0)(1)(0)(1)(2)(0)(1)(1)(0)(1)(2)</math>
 |<math>\varepsilon_1 \times \varepsilon_0^{\varepsilon_0}</math>
-|
-|
 |-
 |<math>(0)(1)(2)(0)(1)(2)(0)(1)(0)(1)(2)(0)(1)(2)</math>
 |<math>\varepsilon_1 ^2</math>
-|
-|
 |-
 |<math>(0)(1)(2)(0)(1)(2)(0)(1)(1)</math>
 |<math>\varepsilon_1 ^\omega</math>
-|
-|
 |-
 |<math>(0)(1)(2)(0)(1)(2)(0)(1)(1)(0)(1)(2)</math>
 |<math>\varepsilon_1 ^{\varepsilon_0}</math>
-|
-|
 |-
 |<math>(0)(1)(2)(0)(1)(2)(0)(1)(1)(0)(1)(2)(0)(1)(2)</math>
 |<math>\varepsilon_1 ^{\varepsilon_1}</math>
-|
-|
 |-
 |<math>(0)(1)(2)(0)(1)(2)(0)(1)(2)</math>
 |<math>\varepsilon_2</math>
-|
-|
 |-
 |<math>(0)(1)(2)(1)</math>
 |<math>\varepsilon_\omega </math>
-|
-|
 |-
 |<math>(0)(1)(2)(1)(0)(1)(2)</math>
 |<math>\varepsilon_{\omega +1} </math>
-|
-|
 |-
 |<math>(0)(1)(2)(1)(0)(1)(2)(0)(1)(2)(1)</math>
 |<math>\varepsilon_{\omega \times 2} </math>
-|
-|
 |-
 |<math>(0)(1)(2)(1)(0)(1)(2)(1)</math>
 |<math>\varepsilon_{\omega ^2} </math>
-|
-|
 |-
 |<math>(0)(1)(2)(1)(1)</math>
 |<math>\varepsilon_{\omega ^\omega} </math>
-|
-|
 |-
 |<math>(0)(1)(2)(1)(1)(2)</math>
 |<math>\varepsilon_{\varepsilon_0} </math>
-|
-|
 |-
 |<math>(0)(1)(2)(1)(1)(2)(0)(1)(2)(1)</math>
 |<math>\varepsilon_{\varepsilon_0 \times \omega} </math>
-|
-|
 |-
 |<math>(0)(1)(2)(1)(1)(2)(0)(1)(2)(1)(0)(1)(2)(1)(1)(2)</math>
 |<math>\varepsilon_{\varepsilon_0 ^2} </math>
-|
-|
 |-
 |<math>(0)(1)(2)(1)(1)(2)(0)(1)(2)(1)(1)</math>
 |<math>\varepsilon_{\varepsilon_0 ^ \omega} </math>
-|
-|
 |-
 |<math>(0)(1)(2)(1)(1)(2)(0)(1)(2)(1)(1)(0)(1)(2)(1)(1)(2)</math>
 |<math>\varepsilon_{\varepsilon_0 ^ {\varepsilon_0}} </math>
-|
-|
 |-
 |<math>(0)(1)(2)(1)(1)(2)(0)(1)(2)(1)(1)(2)</math>
 |<math>\varepsilon_{\varepsilon_1} </math>
-|
-|
 |-
 |<math>(0)(1)(2)(1)(1)(2)(1)</math>
 |<math>\varepsilon_{\varepsilon_\omega} </math>
-|
-|
 |-
 |<math>(0)(1)(2)(1)(1)(2)(1)(1)(2)</math>
 |<math>\varepsilon_{\varepsilon_{\varepsilon_0}}</math>
-|
-|
 |-
 |<math>(0)(1)(2)(1)(2)</math>
 |<math>\zeta_0 </math>
-|
-|
 |-
 |<math>(0)(1)(2)(1)(2)</math>
 |<math>\zeta_0 </math>
-|
-|
 |-
 |<math>(0)(1)(2)(1)(2)(0)(1)(0)(1)(2)(1)(2)</math>
 |<math>\zeta_0 ^2</math>
-|
-|
 |-
 |<math>(0)(1)(2)(1)(2)(0)(1)(1)</math>
 |<math>\zeta_0 ^\omega</math>
-|
-|
 |-
 |<math>(0)(1)(2)(1)(2)(0)(1)(1)(0)(1)(2)(1)(2)</math>
 |<math>\zeta_0 ^{\zeta_0}</math>
-|
-|
 |-
 |<math>(0)(1)(2)(1)(2)(0)(1)(2)</math>
 |<math>\varepsilon_{\zeta_0 +1}</math>
-|
-|
 |-
 |<math>(0)(1)(2)(1)(2)(0)(1)(2)</math>
 |<math>\varepsilon_{\zeta_0 +1}</math>
-|
-|
 |-
 |<math>(0)(1)(2)(1)(2)(0)(1)(2)(0)(1)(2)(1)(1)(2)</math>
 |<math>\varepsilon_{\zeta_0 +\varepsilon_0}</math>
-|
-|
 |-
 |<math>(0)(1)(2)(1)(2)(0)(1)(2)(1)</math>
 |<math>\varepsilon_{\zeta_0 \times \omega}</math>
-|
 |-
 |<math>(0)(1)(2)(1)(2)(0)(1)(2)(1)(0)(1)(2)(1)(2)</math>
 |<math>\varepsilon_{\zeta_0 ^2}</math>
-|
-|
 |-
 |<math>(0)(1)(2)(1)(2)(0)(1)(2)(1)(1)(0)(1)(2)(1)(2)</math>
 |<math>\varepsilon_{\zeta_0 ^{\zeta_0}}</math>
-|
-|
 |-
 |<math>(0)(1)(2)(1)(2)(0)(1)(2)(1)(1)(2)</math>
 |<math>\varepsilon_{\varepsilon_{\zeta_0 +1}}</math>
-|
-|
 |-
 |<math>(0)(1)(2)(1)(2)(0)(1)(2)(1)(2)</math>
 |<math>\zeta_1</math>
-|
-|
 |-
 |<math>(0)(1)(2)(1)(2)(1)</math>
 |<math>\zeta_\omega</math>
-|
-|
 |-
 |<math>(0)(1)(2)(1)(2)(1)(1)(2)</math>
 |<math>\zeta_{\varepsilon_0}</math>
-|
-|
 |-
 |<math>(0)(1)(2)(1)(2)(1)(1)(2)(1)(2)</math>
 |<math>\zeta_{\zeta_0}</math>
-|
-|
 |-
 |<math>(0)(1)(2)(1)(2)(1)(2)</math>
 |<math>\eta_0</math>
-|
-|
 |-
 |<math>(0)(1)(2)(1)(2)(1)(2)(0)(1)(2)</math>
 |<math>\varepsilon_{\eta_0+1}</math>
-|
-|
 |-
 |<math>(0)(1)(2)(1)(2)(1)(2)(0)(1)(2)(1)(2)</math>
 |<math>\zeta_{\eta_0+1}</math>
-|
-|
 |-
 |<math>(0)(1)(2)(1)(2)(1)(2)(0)(1)(2)(1)(2)(1)(2)</math>
 |<math>\eta_1</math>
-|
-|
 |-
 |<math>(0)(1)(2)(1)(2)(1)(2)(1)</math>
 |<math>\eta_\omega</math>
-|
-|
 |-
 |<math>(0)(1)(2)(1)(2)(1)(2)(1)(1)(2)(1)(2)(1)(2)</math>
 |<math>\eta_{\eta_0}</math>
-|
-|
 |-
 |<math>(0)(1)(2)(1)(2)(1)(2)(1)(2)</math>
 |<math>\varphi(4,0)</math>
-|
-|
 |-
 |<math>(0)(1)(2)(2)</math>
 |<math>\varphi(\omega,0)</math>
-|
-|
 |-
 |<math>(0)(1)(2)(2)(0)(1)(2)</math>
 |<math>\varphi(1,\varphi(\omega,0)+1)</math>
-|
-|
 |-
 |<math>(0)(1)(2)(2)(0)(1)(2)(2)</math>
 |<math>\varphi(\omega,1)</math>
-|
-|
 |-
 |<math>(0)(1)(2)(2)(1)</math>
 |<math>\varphi(\omega,\omega)</math>
-|
-|
 |-
 |<math>(0)(1)(2)(2)(1)(1)(2)</math>
 |<math>\varphi(\omega,\varepsilon_0)</math>
-|
-|
 |-
 |<math>(0)(1)(2)(2)(1)(1)(2)(1)(2)(2)</math>
 |<math>\varphi(\omega,\varphi(\omega,0))</math>
-|
-|
 |-
 |<math>(0)(1)(2)(2)(1)(2)</math>
 |<math>\varphi(\omega+1,0)</math>
-|
-|
 |-
 |<math>(0)(1)(2)(2)(1)(2)(1)(2)(2)</math>
 |<math>\varphi(\omega\times 2,0)</math>
-|
-|
 |-
 |<math>(0)(1)(2)(2)(1)(2)(2)</math>
 |<math>\varphi(\omega^2,0)</math>
-|
-|
 |-
 |<math>(0)(1)(2)(2)(2)</math>
 |<math>\varphi(\omega^\omega,0)</math>
-|
-|
 |-
 |<math>(0)(1)(2)(3)</math>
 |<math>\varphi(\varepsilon_0,0)</math>
-|
-|
 |-
 |<math>(0)(1)(2)(3)(1)(2)(3)</math>
 |<math>\varphi(\varepsilon_1,0)</math>
-|
-|
 |-
 |<math>(0)(1)(2)(3)(2)(3)</math>
 |<math>\varphi(\zeta_0,0)</math>
-|
-|
 |-
 |<math>(0)(1)(2)(3)(3)</math>
 |<math>\varphi(\varphi(\omega,0),0)</math>
-|
-|
 |-
 |<math>(0)(1)(2)(3)(4)</math>
 |<math>\varphi(\varphi(\varepsilon_0,0),0)</math>
-|
-|
 |-
 |<math>(0,0)(1,1)</math>
 |<math>\varphi(1,0,0)</math>
-|
-|
 |}
-=== 3. ===
+=== Part 3 ===
 {| class="wikitable"
-|+
 !BHM
-!veblen函数
+!Veblen 函数
 |-
 |<math>(0,0)(1,1)(0,0)</math>