投影 VS 反射稳定

本条目展示投影序数和反射序数、Σ1稳定序数的列表分析

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投影序数	反射序数	常规表示
${\psi }_a(0)$	$min2$	$\mathrm{\Omega }$
${\psi }_a(0)\times 2$	$(1-{)}^{(2)}aft2$	$\mathrm{\Omega }\times 2$
${\psi }_a(0)\times 3$	$2nd(1-{)}^{(2)}aft2$	$\mathrm{\Omega }\times 3$
${\psi }_a(1)$	$(1-{)}^{(2)+1}aft2$	$\mathrm{\Omega }\times \omega$
${\psi }_a(2)$	$(1-{)}^{(2)+2}aft2$	$\mathrm{\Omega }\times {\omega }^2$
${\psi }_a(\omega )$	$(1-{)}^{(2)+\omega }aft2$	$\mathrm{\Omega }\times {\omega }^{\omega }$
${\psi }_a(BO)$	$(1-{)}^{(2)+BO}aft2$	$\mathrm{\Omega }\times BO$
${\psi }_a({\psi }_a(0))$	$(1-{)}^{(1-{)}^{(2)}aft2}aft2$	${\mathrm{\Omega }}^2$
${\psi }_a({\psi }_a(0)+1)$	$(1-{)}^{(1-{)}^{(2)}aft2+1}aft2$	${\mathrm{\Omega }}^2\times \omega$
${\psi }_a({\psi }_a(0)\times 2)$	$(1-{)}^{2nd(1-{)}^{(2)}aft2}aft2$	${\mathrm{\Omega }}^3$
${\psi }_a({\psi }_a(1))$	$(1-{)}^{(1-{)}^{(2)+1}aft2}aft2$	${\mathrm{\Omega }}^{\omega }$
${\psi }_a({\psi }_a({\psi }_a(0)))$	$(1-{)}^{(1-{)}^{(1-{)}^{(2)}aft2}aft2}aft2$	${\mathrm{\Omega }}^{\mathrm{\Omega }}$
${\psi }_a({\psi }_a({\psi }_a({\psi }_a(0))))$	$(1-{)}^{(1-{)}^{(1-{)}^{(1-{)}^{(2)}aft2}aft2}aft2}aft2$	${\mathrm{\Omega }}^{{\mathrm{\Omega }}^{\mathrm{\Omega }}}$
${\psi }_a(a)$	$(1-{)}^{a}aft2$	${\psi }_1({\mathrm{\Omega }}_2)$
${\psi }_a(a)\times 2$	$(1-{)}^{(1-{)}^{a}aft2}aft(1-{)}^{a}aft2$	${\psi }_1({\mathrm{\Omega }}_2)\times 2$
${\psi }_a(a+1)$	$(1-{)}^{(1-{)}^{a}aft2+1}aft(1-{)}^{a}aft2$	${\psi }_1({\mathrm{\Omega }}_2+1)$
${\psi }_a(a+{\psi }_a(a))$	$(1-{)}^{(1-{)}^{(1-{)}^{a}aft2}aft(1-{)}^{a}aft2}aft(1-{)}^{a}aft2$	${\psi }_1({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_2))$
${\psi }_a(a\times 2)$	$2nd(1-{)}^{a}aft2$	${\psi }_1({\mathrm{\Omega }}_2\times 2)$
${\psi }_a(a\times 3)$	$3rd(1-{)}^{a}aft2$	${\psi }_1({\mathrm{\Omega }}_2\times 3)$
${\psi }_a(a\times \omega )$	$(1-{)}^{a+1}aft2$	${\psi }_1({\mathrm{\Omega }}_2\times \omega )$
${\psi }_a(a\times {\psi }_a(a))$	$(1-{)}^{a+(1-{)}^{a}aft2}aft2$	${\psi }_1({\mathrm{\Omega }}_2\times {\psi }_1({\mathrm{\Omega }}_2))$
${\psi }_a(a^2)$	$(1-{)}^{a\times 2}aft2$	${\psi }_1({\mathrm{\Omega }}_2^2)$
${\psi }_a(a^2+a)$	$(1-{)}^{a}aft(1-{)}^{a\times 2}aft2$	${\psi }_1({\mathrm{\Omega }}_2^2+{\mathrm{\Omega }}_2)$
${\psi }_a(a^2+a\times {\psi }_a(a^2))$	$(1-{)}^{a+(1-{)}^{a\times 2}aft2}aft(1-{)}^{a\times 2}aft2$	${\psi }_1({\mathrm{\Omega }}_2^2+{\mathrm{\Omega }}_2\times {\psi }_1({\mathrm{\Omega }}_2^2))$
${\psi }_a(a^2\times 2)$	$2nd(1-{)}^{a\times 2}aft2$	${\psi }_1({\mathrm{\Omega }}_2^2\times 2)$
${\psi }_a(a^2\times \omega )$	$(1-{)}^{a\times 2+1}aft2$	${\psi }_1({\mathrm{\Omega }}_2^2\times \omega )$
${\psi }_a(a^3)$	$(1-{)}^{a\times 3}aft2$	${\psi }_1({\mathrm{\Omega }}_2^3)$
${\psi }_a(a^{\omega })$	$(1-{)}^{a\times \omega }aft2$	${\psi }_1({\mathrm{\Omega }}_2^{\omega })$
${\psi }_a(a^a)$	$(1-{)}^{a^2}aft2$	${\psi }_1({\mathrm{\Omega }}_2^{{\mathrm{\Omega }}_2})$
${\psi }_a(a^{a+1})$	$(1-{)}^{a^2+a}aft2$	${\psi }_1({\mathrm{\Omega }}_2^{{\mathrm{\Omega }}_2+1})$
${\psi }_a(a^{a+\omega })$	$(1-{)}^{a^2+a\times \omega }aft2$	${\psi }_1({\mathrm{\Omega }}_2^{{\mathrm{\Omega }}_2+\omega })$
${\psi }_a(a^{a\times 2})$	$(1-{)}^{a^2\times 2}aft2$	${\psi }_1({\mathrm{\Omega }}_2^{{\mathrm{\Omega }}_2\times 2})$
${\psi }_a(a^{a\times \omega })$	$(1-{)}^{a^2\times \omega }aft2$	${\psi }_1({\mathrm{\Omega }}_2^{{\mathrm{\Omega }}_2\times \omega })$
${\psi }_a(a^{a^2})$	$(1-{)}^{a^3}aft2$	${\psi }_1({\mathrm{\Omega }}_2^{{\mathrm{\Omega }}_2^2})$
${\psi }_a(a^{a^3})$	$(1-{)}^{a^4}aft2$	${\psi }_1({\mathrm{\Omega }}_2^{{\mathrm{\Omega }}_2^3})$
${\psi }_a(a^{a^{\omega }})$	$(1-{)}^{a^{\omega }}aft2$	${\psi }_1({\mathrm{\Omega }}_2^{{\mathrm{\Omega }}_2^{\omega }})$
${\psi }_a(a^{a^a})$	$(1-{)}^{a^a}aft2$	${\psi }_1({\mathrm{\Omega }}_2^{{\mathrm{\Omega }}_2^{{\mathrm{\Omega }}_2}})$
${\psi }_a({\epsilon }_{a+1})$	$(1-{)}^{{\epsilon }_{a+1}}aft2$	${\psi }_1({\mathrm{\Omega }}_3)$
${\psi }_a({\zeta }_{a+1})$	$(1-{)}^{{\zeta }_{a+1}}aft2$	${\psi }_1({\mathrm{\Omega }}_3^2)$
${\psi }_a({\mathrm{\Gamma }}_{a+1})$	$(1-{)}^{{\mathrm{\Gamma }}_{a+1}}aft2$	${\psi }_1({\mathrm{\Omega }}_3^{{\mathrm{\Omega }}_3})$
${\psi }_a(BHO(a+1))$	$(1-{)}^{BHO(a+1)}aft2$	${\psi }_1({\mathrm{\Omega }}_4)$
${\psi }_a(BO(a+1))$	$(1-{)}^{BO(a+1)}aft2$	${\psi }_1({\mathrm{\Omega }}_{\omega })$
${\psi }_a({\mathrm{\Omega }}_{a+1})$	$2nd2$	${\mathrm{\Omega }}_2$
${\psi }_a({\mathrm{\Omega }}_{a+1}+1)$	$(1-{)}^{2nd2}aft2nd2$	${\mathrm{\Omega }}_2\times \omega$
${\psi }_a({\mathrm{\Omega }}_{a+1}+{\psi }_a({\mathrm{\Omega }}_{a+1}))$	$(1-{)}^{(1-{)}^{2nd2}aft2nd2}aft2nd2$	${\mathrm{\Omega }}_2^2$
${\psi }_a({\mathrm{\Omega }}_{a+1}+{\psi }_a({\mathrm{\Omega }}_{a+1})\times 2)$	$(1-{)}^{2nd(1-{)}^{2nd2}aft2nd2}aft2nd2$	${\mathrm{\Omega }}_2^3$
${\psi }_a({\mathrm{\Omega }}_{a+1}+{\psi }_a({\mathrm{\Omega }}_{a+1}+1))$	$(1-{)}^{(1-{)}^{Ordaft2nd2}aft2nd2}aft2nd2$	${\mathrm{\Omega }}_2^{\omega }$
${\psi }_a({\mathrm{\Omega }}_{a+1}+{\psi }_a({\mathrm{\Omega }}_{a+1}+{\psi }_a({\mathrm{\Omega }}_{a+1})))$	$(1-{)}^{(1-{)}^{(1-{)}^{2nd2}aft2nd2}aft2nd2}aft2nd2$	${\mathrm{\Omega }}_2^{{\mathrm{\Omega }}_2}$
${\psi }_a({\mathrm{\Omega }}_{a+1}+a)$	$(1-{)}^{a}aft2$	${\psi }_2({\mathrm{\Omega }}_3)$
${\psi }_a({\mathrm{\Omega }}_{a+1}+a^a)$	$(1-{)}^{a^2}aft2$	${\psi }_2({\mathrm{\Omega }}_3^{{\mathrm{\Omega }}_3})$
${\psi }_a({\mathrm{\Omega }}_{a+1}+{\epsilon }_{a+1})$	$(1-{)}^{{\epsilon }_{a+1}}aft2$	${\psi }_2({\mathrm{\Omega }}_4)$
${\psi }_a({\mathrm{\Omega }}_{a+1}+BO(a+1))$	$(1-{)}^{BO(a+1)}aft2$	${\psi }_2({\mathrm{\Omega }}_{\omega })$
${\psi }_a({\mathrm{\Omega }}_{a+1}\times 2)$	$2nd2$	${\mathrm{\Omega }}_3$
${\psi }_a({\mathrm{\Omega }}_{a+1}\times 2+a)$	$(1-{)}^{a}aft2nd2$	${\psi }_3({\mathrm{\Omega }}_4)$
${\psi }_a({\mathrm{\Omega }}_{a+1}\times 3)$	$3rd2$	${\mathrm{\Omega }}_4$
${\psi }_a({\mathrm{\Omega }}_{a+1}\times \omega )$	$1-2$	${\mathrm{\Omega }}_{\omega }$
${\psi }_a({\mathrm{\Omega }}_{a+1}\times \omega \times 2)$	$2nd1-2$	${\mathrm{\Omega }}_{\omega \times 2}$
${\psi }_a({\mathrm{\Omega }}_{a+1}\times {\omega }^2)$	$1-1-2$	${\mathrm{\Omega }}_{{\omega }^2}$
${\psi }_a({\mathrm{\Omega }}_{a+1}\times {\omega }^{\omega })$	$(1-{)}^{\omega }2$	${\mathrm{\Omega }}_{{\omega }^{\omega }}$
${\psi }_a({\mathrm{\Omega }}_{a+1}\times {\psi }_a(0))$	$(1-{)}^{(2)}2$	${\mathrm{\Omega }}_{\mathrm{\Omega }}$
${\psi }_a({\mathrm{\Omega }}_{a+1}\times {\psi }_a({\mathrm{\Omega }}_{a+1}\times \omega ))$	$(1-{)}^{1-2}2$	${\mathrm{\Omega }}_{{\mathrm{\Omega }}_{\omega }}$
${\psi }_a({\mathrm{\Omega }}_{a+1}\times a)$	$(1-{)}^{a}2$	$OFP={\psi }_I(I)$
${\psi }_a({\mathrm{\Omega }}_{a+1}\times a+{\mathrm{\Omega }}_{a+1})$	$2aft(1-{)}^{a}2$	${\mathrm{\psi }}_{\mathrm{I}}\mathrm{(}\mathrm{I}\mathrm{+}\mathrm{1}\mathrm{)}$
${\psi }_a({\mathrm{\Omega }}_{a+1}\times a+{\mathrm{\Omega }}_{a+1}\times {\psi }_a({\mathrm{\Omega }}_{a+1}\times a))$	$(1-{)}^{(1-{)}^{a}2}2aft(1-{)}^{a}2$	${\mathrm{\psi }}_{\mathrm{I}}\mathrm{(}\mathrm{I}\mathrm{+}{\mathrm{\psi }}_{\mathrm{I}}\mathrm{(}\mathrm{I}\mathrm{)}\mathrm{)}$
${\psi }_a({\mathrm{\Omega }}_{a+1}\times a\times 2)$	$2nd(1-{)}^{a}2$	${\mathrm{\psi }}_{\mathrm{I}}\mathrm{(}\mathrm{I}\mathrm{\times }\mathrm{2}\mathrm{)}$
${\psi }_a({\mathrm{\Omega }}_{a+1}\times a\times \omega )$	$(1-{)}^{a+1}2$	${\mathrm{\psi }}_{\mathrm{I}}\mathrm{(}\mathrm{I}\mathrm{\times }\mathrm{\omega }\mathrm{)}$
${\psi }_a({\mathrm{\Omega }}_{a+1}\times a\times {\psi }_a({\mathrm{\Omega }}_{a+1}\times a))$	$(1-{)}^{a+(1-{)}^{a}2}2$	${\mathrm{\psi }}_{\mathrm{I}}\mathrm{(}\mathrm{I}\mathrm{\times }{\mathrm{\psi }}_{\mathrm{I}}\mathrm{(}\mathrm{I}\mathrm{)}\mathrm{)}$
${\psi }_a({\mathrm{\Omega }}_{a+1}\times a^2)$	$(1-{)}^{a\times 2}2$	${\mathrm{\psi }}_{\mathrm{I}}\mathrm{(}{\mathrm{I}}^{\mathrm{2}}\mathrm{)}$
${\psi }_a({\mathrm{\Omega }}_{a+1}\times a^3)$	$(1-{)}^{a\times 3}2$	${\mathrm{\psi }}_{\mathrm{I}}\mathrm{(}{\mathrm{I}}^{\mathrm{3}}\mathrm{)}$
${\psi }_a({\mathrm{\Omega }}_{a+1}\times a^a)$	$(1-{)}^{a^2}2$	${\mathrm{\psi }}_{\mathrm{I}}\mathrm{(}{\mathrm{I}}^{\mathrm{I}}\mathrm{)}$
${\psi }_a({\mathrm{\Omega }}_{a+1}\times {\epsilon }_{a+1})$	$(1-{)}^{{\epsilon }_{a+1}}2$	${\mathrm{\psi }}_{\mathrm{I}}\mathrm{(}{\mathrm{\Omega }}_{\mathrm{I}\mathrm{+}\mathrm{1}}\mathrm{)}$
${\psi }_a({\mathrm{\Omega }}_{a+1}\times BO(a+1))$	$(1-{)}^{BO(a+1)}2$	${\mathrm{\psi }}_{\mathrm{I}}\mathrm{(}{\mathrm{\Omega }}_{\mathrm{I}\mathrm{+}\mathrm{\omega }}\mathrm{)}$
${\psi }_a({\mathrm{\Omega }}_{a+1}\times SHO(a+1))$	$(1-{)}^{SHO(a+1)}2$	${\mathrm{\psi }}_{\mathrm{I}}\mathrm{(}{\mathrm{\psi }}_{\mathrm{H}}\mathrm{(}{\mathrm{\epsilon }}_{\mathrm{H}\mathrm{+}\mathrm{1}}\mathrm{)}\mathrm{)}$
${\psi }_a({\mathrm{\Omega }}_{a+1}^2)$	$21-2$	$\mathrm{I}$
${\psi }_a({\mathrm{\Omega }}_{a+1}^2+{\mathrm{\Omega }}_{a+1})$	$2aft21-2$	${\mathrm{\Omega }}_{\mathrm{I}\mathrm{+}\mathrm{1}}$
${\psi }_a({\mathrm{\Omega }}_{a+1}^2+{\mathrm{\Omega }}_{a+1}\times \omega )$	$1-2aft21-2$	${\mathrm{\Omega }}_{\mathrm{I}\mathrm{+}\mathrm{\omega }}$
${\psi }_a({\mathrm{\Omega }}_{a+1}^2+{\mathrm{\Omega }}_{a+1}\times {\psi }_a({\mathrm{\Omega }}_{a+1}^2))$	$(1-{)}^{21-2}2aft21-2$	${\mathrm{\Omega }}_{\mathrm{I}\mathrm{\times }\mathrm{2}}$
${\psi }_a({\mathrm{\Omega }}_{a+1}^2+{\mathrm{\Omega }}_{a+1}\times {\psi }_a({\mathrm{\Omega }}_{a+1}^2+1))$	$(1-{)}^{Ordaft21-2}2aft21-2$	${\mathrm{\Omega }}_{\mathrm{I}\mathrm{\times }\mathrm{\omega }}$
${\psi }_a({\mathrm{\Omega }}_{a+1}^2+{\mathrm{\Omega }}_{a+1}\times {\psi }_a({\mathrm{\Omega }}_{a+1}^2+{\psi }_a({\mathrm{\Omega }}_{a+1}^2)))$	$(1-{)}^{(1-{)}^{21-2}aft21-2}2aft21-2$	${\mathrm{\Omega }}_{{\mathrm{I}}^{\mathrm{2}}}$
${\psi }_a({\mathrm{\Omega }}_{a+1}^2+{\mathrm{\Omega }}_{a+1}\times {\psi }_a({\mathrm{\Omega }}_{a+1}^2+a))$	$(1-{)}^{(1-{)}^{a}aft21-2}2aft21-2$	${\mathrm{\Omega }}_{{\mathrm{\epsilon }}_{\mathrm{I}\mathrm{+}\mathrm{1}}}$