BHM分析：修订间差异

2025年7月11日 (五) 15:10的版本

本条目展示BHM的强度的列表分析

1.


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

2.


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

3.


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

@@ 第5行： / 第5行： @@
 |+
 !BHM
-!
+!veblen函数
 !
 !
@@ 第209行： / 第209行： @@
 |+
 !BHM
-!
+!veblen函数
 !
 !
@@ 第601行： / 第601行： @@
 |
 |
+|}
+=== 3. ===
+{| class="wikitable"
+|+
+!BHM
+!veblen函数
+|-
+|<math>(0,0)(1,1)(0,0)</math>
+|<math>\varphi(1,0,0)+1</math>
+|-
+|<math>(0,0)(1,1)(0,0)(0,0)(1,1)</math>
+|<math>\varphi(1,0,0)\times2</math>
+|-
+|<math>(0,0)(1,1)(0,0)(1,0)</math>
+|<math>\omega^{\varphi(1,0,0)+1}</math>
+|-
+|<math>(0,0)(1,1)(0,0)(1,0)(1,0)</math>
+|<math>\omega^{\omega^{\varphi(1,0,0)+1}}</math>
+|-
+|<math>(0,0)(1,1)(0,0)(1,0)(2,0)</math>
+|<math>\varphi(1,\varphi(1,0,0)+1)</math>
+|-
+|<math>(0,0)(1,1)(0,0)(1,0)(2,0)(0,0)(1,1)</math>
+|<math>\varphi(1,\varphi(1,0,0)\times2)</math>
+|-
+|<math>(0,0)(1,1)(0,0)(1,0)(2,0)(1,0)(1,0)(2,0)</math>
+|<math>\varphi(1,\varphi(1,\varphi(1,0,0)+1))</math>
+|-
+|<math>(0,0)(1,1)(0,0)(1,0)(2,0)(1,0)(2,0)</math>
+|<math>\varphi(2,\varphi(1,0,0)+1)</math>
+|-
+|<math>(0,0)(1,1)(0,0)(1,0)(2,0)(2,0)</math>
+|<math>\varphi(\omega,\varphi(1,0,0)+1)</math>
+|-
+|<math>(0,0)(1,1)(0,0)(1,0)(2,0)(2,0)(1,0)(2,0)</math>
+|<math>\varphi(\omega+1,\varphi(1,0,0)+1)</math>
+|-
+|<math>(0,0)(1,1)(0,0)(1,0)(2,0)(2,0)(1,0)(2,0)(2,0)</math>
+|<math>\varphi(\omega^2,\varphi(1,0,0)+1)</math>
+|-
+|<math>(0,0)(1,1)(0,0)(1,0)(2,0)(2,0)(2,0)</math>
+|<math>\varphi(\omega^\omega,\varphi(1,0,0)+1)</math>
+|-
+|<math>(0,0)(1,1)(0,0)(1,0)(2,0)(3,0)</math>
+|<math>\varphi(\varphi(1,0),\varphi(1,0,0)+1)</math>
+|-
+|<math>(0,0)(1,1)(0,0)(1,0)(2,0)(3,0)(4,0)</math>
+|<math>\varphi(\varphi(\varphi(1,0),0),\varphi(1,0,0)+1)</math>
+|-
+|<math>(0,0)(1,1)(0,0)(1,0)(2,0)(3,0)(4,0)(5,0)</math>
+|<math>\varphi (\varphi (\varphi(\varphi(1,0),0),0),\varphi(1,0,0)+1)</math>
+|-
+|<math>(0,0)(1,1)(0,0)(1,1)</math>
+|<math>\varphi(\varphi(1,0,0),1)</math>
+|-
+|<math>(0,0)(1,1)(0,0)(1,1)(0,0)(1,1)</math>
+|<math>\varphi(\varphi(1,0,0),2)</math>
+|-
+|<math>(0,0)(1,1)(1,0)</math>
+|<math>\varphi(\varphi(1,0,0),\omega)</math>
+|-
+|<math>(0,0)(1,1)(1,0)(0,0)(1,1)</math>
+|<math>\varphi(\varphi(1,0,0),\omega+1)</math>
+|-
+|<math>(0,0)(1,1)(1,0)(0,0)(1,1)(0,0)(1,1)(1,0)</math>
+|<math>\varphi(\varphi(1,0,0),\omega\times2)</math>
+|-
+|<math>(0,0)(1,1)(1,0)(0,0)(1,1)(1,0)</math>
+|<math>\varphi(\varphi(1,0,0),\omega^2)</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)</math>
+|<math>\varphi(\varphi(1,0,0),\omega^\omega)</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(1,0)</math>
+|<math>\varphi(\varphi(1,0,0),\omega^{\omega^\omega})</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)</math>
+|<math>\varphi(\varphi(1,0,0),\varphi(1,0))</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(1,0)(2,0)</math>
+|<math>\varphi(\varphi(1,0,0),\varphi(2,0))</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(2,0)</math>
+|<math>\varphi(\varphi(1,0,0),\varphi(\omega,0))</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,0)</math>
+|<math>\varphi(\varphi(1,0,0),\varphi(\varphi(1,0),0))</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,0)(4,0)</math>
+|<math>\varphi(\varphi(1,0,0),\varphi(\varphi(\varphi(1,0),0),0))</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)</math>
+|<math>\varphi(\varphi(1,0,0),\varphi(1,0,0))</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(0,0)(1,1)</math>
+|<math>\varphi(\varphi(1,0,0),\varphi(1,0,0)+1)</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(0,0)(1,1)(0,0)(1,1)</math>
+|<math>\varphi(\varphi(1,0,0),\varphi(1,0,0)+2)</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(0,0)(1,1)(0,0)(1,1)(1,0)</math>
+|<math>\varphi(\varphi(1,0,0),\varphi(1,0,0)+\omega)</math>
+|-
+|<math>(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)</math>
+|<math>\varphi(\varphi(1,0,0),\varphi(1,0,0)\times2)</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(0,0)(1,1)(1,0)</math>
+|<math>\varphi(\varphi(1,0,0),\omega^{\varphi(1,0,0)+1})</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(0,0)(1,1)(1,0)(1,0)(2,0)</math>
+|<math>\varphi(\varphi(1,0,0),\varphi(1,\varphi(1,0,0)+1))</math>
+|-
+|<math>(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)</math>
+|<math>\varphi(\varphi(1,0,0),\varphi(2,\varphi(1,0,0)+1))</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(0,0)(1,1)(1,0)(1,0)(2,0)(2,0)</math>
+|<math>\varphi(\varphi(1,0,0),\varphi(\omega,\varphi(1,0,0)+1))</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(0,0)(1,1)(1,0)(1,0)(2,0)(3,0)</math>
+|<math>\varphi(\varphi(1,0,0),\varphi(\varphi(1,0),\varphi(1,0,0)+1))</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)</math>
+|<math>\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0),1))</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)</math>
+|<math>\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0),\omega))</math>
+|-
+|<math>(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)</math>
+|<math>\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0),\omega+1))</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(1,0)</math>
+|<math>\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0),\omega^\omega))</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(1,0)(2,0)</math>
+|<math>\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0),\varphi(1,0)))</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(1,0)(2,0)(2,0)</math>
+|<math>\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0),\varphi(\omega,0)))</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(1,0)(2,0)(3,1)</math>
+|<math>\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0),\varphi(1,0,0)))</math>
+|-
+|<math>(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)</math>
+|<math>\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0),1)))</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)</math>
+|<math>\varphi(\varphi(1,0,0)+1,0)</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)(0,0)(1,1)</math>
+|<math>\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0)+1,0)+1)</math>
+|-
+|<math>(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)</math>
+|<math>\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0)+1,0)\times2)</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)(0,0)(1,1)(1,0)</math>
+|<math>\varphi(\varphi(1,0,0),\omega^{\varphi(\varphi(1,0,0)+1,0)+1})</math>
+|-
+|<math>(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)</math>
+|<math>\varphi(\varphi(1,0,0),\varphi(1,\varphi(\varphi(1,0,0)+1,0)+1))</math>
+|-
+|<math>(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)</math>
+|<math>\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0)+1,0)+1))</math>
+|-
+|<math>(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)</math>
+|<math>\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0)+1,0)\times2))</math>
+|-
+|<math>(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)</math>
+|<math>\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0),\varphi(1,\varphi(\varphi(1,0,0)+1,0)+1)))</math>
+|-
+|<math>(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)</math>
+|<math>\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0)+1,0)+1)))</math>
+|-
+|<math>(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)</math>
+|<math>\varphi(\varphi(1,0,0)+1,1)</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)(1,0)</math>
+|<math>\varphi(\varphi(1,0,0)+1,\omega)</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)(1,0)(1,0)(2,0)</math>
+|<math>\varphi(\varphi(1,0,0)+1,\varphi(1,0))</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)(1,0)(1,0)(2,0)(3,1)</math>
+|<math>\varphi(\varphi(1,0,0)+1,\varphi(1,0,0))</math>
+|-
+|<math>(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)</math>
+|<math>\varphi(\varphi(1,0,0)+1,\varphi(\varphi(1,0,0)+1,0))</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)(1,0)(2,0)</math>
+|<math>\varphi(\varphi(1,0,0)+2,0)</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)(1,0)(2,0)(2,0)</math>
+|<math>\varphi(\varphi(1,0,0)+\omega,0)</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)(1,0)(2,0)(3,0)</math>
+|<math>\varphi(\varphi(1,0,0)+\varphi(1,0),0)</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)(1,0)(2,0)(3,1)</math>
+|<math>\varphi(\varphi(1,0,0)\times2,0)</math>
+|-
+|<math>(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)</math>
+|<math>\varphi(\varphi(1,0,0)\times3,0)</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)(2,0)</math>
+|<math>\varphi(\omega^{\varphi(1,0,0)+1},0)</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)(3,0)</math>
+|<math>\varphi(\varphi(1,\varphi(1,0,0)+1),0)</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)(3,1)</math>
+|<math>\varphi(\varphi(\varphi(1,0,0),1),0)</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)(3,1)(1,0)(2,0)</math>
+|<math>\varphi(\varphi(\varphi(1,0,0),1)+1,0)</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)(3,1)(1,0)(2,0)(2,0)</math>
+|<math>\varphi(\omega^{\varphi(\varphi(1,0,0),1)+1},0)</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)(3,1)(1,0)(2,0)(3,0)</math>
+|<math>\varphi(\varphi(1,\varphi(\varphi(1,0,0),1)+1),0)</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(1,0)(2,0)(3,1)(1,0)(2,0)(3,1)</math>
+|<math>\varphi(\varphi(\varphi(1,0,0),2),0)</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(2,0)</math>
+|<math>\varphi(\varphi(\varphi(1,0,0),\omega),0)</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(2,0)(1,0)(2,0)(3,1)</math>
+|<math>\varphi(\varphi(\varphi(1,0,0),\omega+1),0)</math>
+|-
+|<math>(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)</math>
+|<math>\varphi(\varphi(\varphi(1,0,0),\omega\times2),0)</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(2,0)(2,0)</math>
+|<math>\varphi(\varphi(\varphi(1,0,0),\omega^\omega),0)</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(2,0)(2,0)(3,0)</math>
+|<math>\varphi(\varphi(\varphi(1,0,0),\varphi(1,0)),0)</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(2,0)(2,0)(3,1)</math>
+|<math>\varphi(\varphi(\varphi(1,0,0),\varphi(1,0,0)),0)</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(2,0)(2,0)(3,1)(1,0)(2,0)(3,1)</math>
+|<math>\varphi(\varphi(\varphi(1,0,0),\varphi(1,0,0)+1),0)</math>
+|-
+|<math>(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)</math>
+|<math>\varphi(\varphi(\varphi(1,0,0),\omega^{\varphi(1,0,0)+1}),0)</math>
+|-
+|<math>(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)</math>
+|<math>\varphi(\varphi(\varphi(1,0,0),\varphi(1,\varphi(1,0,0)+1)),0)</math>
+|-
+|<math>(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)</math>
+|<math>\varphi(\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0),1)),0)</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(2,0)(2,0)(3,1)(2,0)</math>
+|<math>\varphi(\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0),\omega)),0)</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(2,0)(2,0)(3,1)(2,0)(2,0)(3,1)</math>
+|<math>\varphi(\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0),\varphi(1,0,0))),0)</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(2,0)(3,0)</math>
+|<math>\varphi(\varphi(\varphi(1,0,0)+1,0),0)</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(2,0)(3,0)(2,0)(3,0)</math>
+|<math>\varphi(\varphi(\varphi(1,0,0)+2,0),0)</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(2,0)(3,0)(2,0)(3,1)</math>
+|<math>\varphi(\varphi(\varphi(1,0,0)\times2,0),0)</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(2,0)(3,0)(3,0)</math>
+|<math>\varphi(\varphi(\omega^{\varphi(1,0,0)+1},0),0)</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(2,0)(3,1)</math>
+|<math>\varphi(\varphi(\varphi(\varphi(1,0,0),1),0),0)</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(3,0)</math>
+|<math>\varphi(\varphi(\varphi(\varphi(1,0,0),\omega),0),0)</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(3,0)(3,0)(4,0)</math>
+|<math>\varphi(\varphi(\varphi(\varphi(1,0,0),\varphi(1,0)),0),0)</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(3,0)(3,0)(4,0)(5,1)</math>
+|<math>\varphi(\varphi(\varphi(\varphi(1,0,0),\varphi(1,0,0)),0),0)</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(3,0)(3,0)(4,0)(5,1)(2,0)(3,1)</math>
+|<math>\varphi(\varphi(\varphi(\varphi(1,0,0),\varphi(1,0,0)+1),0),0)</math>
+|-
+|<math>(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)</math>
+|<math>\varphi(\varphi(\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0),1)),0),0)</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(3,0)(3,0)(4,0)(5,1)(3,0)</math>
+|<math>\varphi(\varphi(\varphi(\varphi(1,0,0),\varphi(\varphi(1,0,0),\omega)),0),0)</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(3,0)(3,0)(4,0)(5,1)(3,0)(4,0)</math>
+|<math>\varphi(\varphi(\varphi(\varphi(1,0,0)+1,0),0),0)</math>
+|-
+|<math>(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)</math>
+|<math>\varphi(\varphi(\varphi(\varphi(1,\varphi(1,0,0)+1),0),0),0)</math>
+|-
+|<math>(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)</math>
+|<math>\varphi(\varphi(\varphi(\varphi(\varphi(1,0,0),1),0),0),0)</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,0)(3,1)(3,0)(3,0)(4,0)(5,1)(4,0)(5,1)</math>
+|<math>\varphi(\varphi(\varphi(\varphi(\varphi(\varphi(1,0,0),1),0),0),0),0)</math>
+|-
+|<math>(0,0)(1,1)(1,0)(1,0)(2,1)</math>
+|<math>\varphi(1,0,1)</math>
 |}
 [[分类:分析]]