投影 VS 反射稳定:修订间差异
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本条目展示[[投影序数]]和[[反射序数]]、[[ | 本条目展示[[投影序数]]和[[反射序数]]、[[Σ1稳定序数]]的列表分析 | ||
=== 1 === | |||
{| class="wikitable" | {| class="wikitable" | ||
|+ | |+ | ||
!投影序数 | !投影序数 | ||
! | !反射序数 | ||
!常规表示 | |||
|- | |- | ||
|<math>\ | |<math>\psi_a(0)</math> | ||
|<math> | |<math>min~2</math> | ||
|<math>\Omega</math> | |||
|- | |- | ||
|<math>\ | |<math>\psi_a(0)\times2</math> | ||
|<math> | |<math>(1-)^{(2)}~aft~2</math> | ||
|<math>\Omega\times2</math> | |||
|- | |- | ||
|<math>\ | |<math>\psi_a(0)\times3</math> | ||
|<math> | |<math>2nd~(1-)^{(2)}~aft~2</math> | ||
|<math>\Omega\times3</math> | |||
|- | |- | ||
|<math>\ | |<math>\psi_a(1)</math> | ||
|<math>1-1</math> | |<math>(1-)^{(2)+1}~aft~2</math> | ||
|<math>\Omega\times\omega</math> | |||
|- | |- | ||
|<math>\ | |<math>\psi_a(2)</math> | ||
|<math>1~aft~ | |<math>(1-)^{(2)+2}~aft~2</math> | ||
|<math>\Omega\times\omega^2</math> | |||
|- | |- | ||
|<math>\omega^2+\omega | |<math>\psi_a(\omega)</math> | ||
|<math> | |<math>(1-)^{(2)+\omega}~aft~2</math> | ||
|<math>\Omega\times\omega^\omega</math> | |||
|- | |- | ||
|<math>\ | |<math>\psi_a(BO)</math> | ||
|<math> | |<math>(1-)^{(2)+BO}~aft~2</math> | ||
|<math>\Omega\times BO</math> | |||
|- | |- | ||
|<math>\ | |<math>\psi_a(\psi_a(0))</math> | ||
|<math>1-1- | |<math>(1-)^{(1-)^{(2)}~aft~2}~aft~2</math> | ||
|<math>\Omega^2</math> | |||
|- | |- | ||
|<math>\ | |<math>\psi_a(\psi_a(0)+1)</math> | ||
|<math>(1-)^\omega</math> | |<math>(1-)^{(1-)^{(2)}~aft~2+1}~aft~2</math> | ||
|<math>\Omega^2\times\omega</math> | |||
|- | |- | ||
|<math>\ | |<math>\psi_a(\psi_a(0)\times2)</math> | ||
|<math>(1-)^{ | |<math>(1-)^{2nd~(1-)^{(2)}~aft~2}~aft~2</math> | ||
|<math>\Omega^3</math> | |||
|- | |- | ||
|<math>\ | |<math>\psi_a(\psi_a(1))</math> | ||
|<math>(1-)^{1-1}</math> | |<math>(1-)^{(1-)^{(2)+1}~aft~2}~aft~2</math> | ||
|<math>\Omega^\omega</math> | |||
|- | |- | ||
|<math>\ | |<math>\psi_a(\psi_a(\psi_a(0)))</math> | ||
|<math>(1-)^{(1-)^\ | |<math>(1-)^{(1-)^{(1-)^{(2)}~aft~2}~aft~2}~aft~2</math> | ||
|<math>\Omega^\Omega</math> | |||
|- | |- | ||
|<math>\ | |<math>\psi_a(\psi_a(\psi_a(\psi_a(0))))</math> | ||
|<math>(1-)^ | |<math>(1-)^{(1-)^{(1-)^{(1-)^{(2)}~aft~2}~aft~2}~aft~2}~aft~2</math> | ||
|<math>\Omega^{\Omega^\Omega}</math> | |||
|- | |- | ||
|<math>\ | |<math>\psi_a(a)</math> | ||
|<math> | |<math>(1-)^a~aft~2</math> | ||
|<math>\psi_1(\Omega_2)</math> | |||
|- | |- | ||
|<math>\ | |<math>\psi_a(a)\times2</math> | ||
|<math>(1-)^{(1-)^a | |<math>(1-)^{(1-)^a~aft~2}~aft~(1-)^a~aft~2</math> | ||
|<math>\psi_1(\Omega_2)\times2</math> | |||
|- | |- | ||
|<math>\ | |<math>\psi_a(a+1)</math> | ||
|<math> | |<math>(1-)^{(1-)^a~aft~2+1}~aft~(1-)^a~aft~2</math> | ||
|<math>\psi_1(\Omega_2+1)</math> | |||
|- | |- | ||
|<math>\ | |<math>\psi_a(a+\psi_a(a))</math> | ||
|<math>(1-)^{a | |<math>(1-)^{(1-)^{(1-)^a~aft~2}~aft~(1-)^a~aft~2}~aft~(1-)^a~aft~2</math> | ||
|<math>\psi_1(\Omega_2+\psi_1(\Omega_2))</math> | |||
|- | |- | ||
|<math>\ | |<math>\psi_a(a\times2)</math> | ||
|<math>(1-)^ | |<math>2nd~(1-)^a~aft~2</math> | ||
|<math>\psi_1(\Omega_2\times2)</math> | |||
|- | |- | ||
|<math>\ | |<math>\psi_a(a\times3)</math> | ||
|<math>(1-)^ | |<math>3rd~(1-)^a~aft~2</math> | ||
|<math>\psi_1(\Omega_2\times3)</math> | |||
|- | |- | ||
|<math>\ | |<math>\psi_a(a\times\omega)</math> | ||
|<math>(1-)^{a\times\omega | |<math>(1-)^{a+1}~aft~2</math> | ||
|<math>\psi_1(\Omega_2\times\omega)</math> | |||
|- | |- | ||
|<math>\ | |<math>\psi_a(a\times\psi_a(a))</math> | ||
|<math>(1-)^{a^2}</math> | |<math>(1-)^{a+(1-)^a~aft~2}~aft~2</math> | ||
|<math>\psi_1(\Omega_2\times\psi_1(\Omega_2))</math> | |||
|- | |- | ||
|<math>\ | |<math>\psi_a(a^2)</math> | ||
|<math>(1-)^{a | |<math>(1-)^{a\times2}~aft~2</math> | ||
|<math>\psi_1(\Omega_2^2)</math> | |||
|- | |- | ||
|<math>\ | |<math>\psi_a(a^2+a)</math> | ||
|<math>(1-)^{a^ | |<math>(1-)^a~aft~(1-)^{a\times2}~aft~2</math> | ||
|<math>\psi_1(\Omega_2^2+\Omega_2)</math> | |||
|- | |- | ||
|<math>\ | |<math>\psi_a(a^2+a\times\psi_a(a^2))</math> | ||
|<math>(1-)^{a^\ | |<math>(1-)^{a+(1-)^{a\times2}~aft~2}~aft~(1-)^{a\times2}~aft~2</math> | ||
|<math>\psi_1(\Omega_2^2+\Omega_2\times\psi_1(\Omega_2^2))</math> | |||
|- | |- | ||
|<math>\ | |<math>\psi_a(a^2\times2)</math> | ||
|<math>(1-)^{a^ | |<math>2nd~(1-)^{a\times2}~aft~2</math> | ||
|<math>\psi_1(\Omega_2^2\times2)</math> | |||
|- | |- | ||
|<math>\ | |<math>\psi_a(a^2\times\omega)</math> | ||
|<math>(1-)^{\ | |<math>(1-)^{a\times2+1}~aft~2</math> | ||
|<math>\psi_1(\Omega_2^2\times\omega)</math> | |||
|- | |- | ||
|<math>\ | |<math>\psi_a(a^3)</math> | ||
|<math>(1-)^{\ | |<math>(1-)^{a\times3}~aft~2</math> | ||
|<math>\psi_1(\Omega_2^3)</math> | |||
|- | |- | ||
| | |<math>\psi_a(a^\omega)</math> | ||
|<math>(1-)^{\ | |<math>(1-)^{a\times\omega}~aft~2</math> | ||
|<math>\psi_1(\Omega_2^\omega)</math> | |||
|- | |- | ||
| | |<math>\psi_a(a^a)</math> | ||
|<math>(1-)^ | |<math>(1-)^{a^2}~aft~2</math> | ||
|<math>\psi_1(\Omega_2^{\Omega_2})</math> | |||
|- | |- | ||
| | |<math>\psi_a(a^{a+1})</math> | ||
|<math>(1-)^ | |<math>(1-)^{a^2+a}~aft~2</math> | ||
|<math>\psi_1(\Omega_2^{\Omega_2+1})</math> | |||
|- | |- | ||
| | |<math>\psi_a(a^{a+\omega})</math> | ||
|<math>(1-)^{\ | |<math>(1-)^{a^2+a\times\omega}~aft~2</math> | ||
|<math>\psi_1(\Omega_2^{\Omega_2+\omega})</math> | |||
|- | |||
|<math>\psi_a(a^{a\times2})</math> | |||
|<math>(1-)^{a^2\times2}~aft~2</math> | |||
|<math>\psi_1(\Omega_2^{\Omega_2\times2})</math> | |||
|- | |||
|<math>\psi_a(a^{a\times\omega})</math> | |||
|<math>(1-)^{a^2\times\omega}~aft~2</math> | |||
|<math>\psi_1(\Omega_2^{\Omega_2\times\omega})</math> | |||
|- | |||
|<math>\psi_a(a^{a^2})</math> | |||
|<math>(1-)^{a^3}~aft~2</math> | |||
|<math>\psi_1(\Omega_2^{\Omega_2^2})</math> | |||
|- | |||
|<math>\psi_a(a^{a^3})</math> | |||
|<math>(1-)^{a^4}~aft~2</math> | |||
|<math>\psi_1(\Omega_2^{\Omega_2^3})</math> | |||
|- | |||
|<math>\psi_a(a^{a^\omega})</math> | |||
|<math>(1-)^{a^\omega}~aft~2</math> | |||
|<math>\psi_1(\Omega_2^{\Omega_2^\omega})</math> | |||
|- | |||
|<math>\psi_a(a^{a^a})</math> | |||
|<math>(1-)^{a^a}~aft~2</math> | |||
|<math>\psi_1(\Omega_2^{\Omega_2^{\Omega_2}})</math> | |||
|- | |||
|<math>\psi_a(\varepsilon_{a+1})</math> | |||
|<math>(1-)^{\varepsilon_{a+1}}~aft~2</math> | |||
|<math>\psi_1(\Omega_3)</math> | |||
|- | |||
|<math>\psi_a(\zeta_{a+1})</math> | |||
|<math>(1-)^{\zeta_{a+1}}~aft~2</math> | |||
|<math>\psi_1(\Omega_3^2)</math> | |||
|- | |||
|<math>\psi_a(\Gamma_{a+1})</math> | |||
|<math>(1-)^{\Gamma_{a+1}}~aft~2</math> | |||
|<math>\psi_1(\Omega_3^{\Omega_3})</math> | |||
|- | |||
|<math>\psi_a(BHO(a+1))</math> | |||
|<math>(1-)^{BHO(a+1)}~aft~2</math> | |||
|<math>\psi_1(\Omega_4)</math> | |||
|- | |||
|<math>\psi_a(BO(a+1))</math> | |||
|<math>(1-)^{BO(a+1)}~aft~2</math> | |||
|<math>\psi_1(\Omega_\omega)</math> | |||
|- | |||
|<math>\psi_a(\Omega_{a+1})</math> | |||
|<math>2nd~2</math> | |||
|<math>\Omega_2</math> | |||
|- | |||
|<math>\psi_a(\Omega_{a+1}+1)</math> | |||
|<math>(1-)^{2nd~2}~aft~2nd~2</math> | |||
|<math>\Omega_2\times\omega</math> | |||
|- | |||
|<math>\psi_a(\Omega_{a+1}+\psi_a(\Omega_{a+1}))</math> | |||
|<math>(1-)^{(1-)^{2nd~2}~aft~2nd~2}~aft~2nd~2</math> | |||
|<math>\Omega_2^2</math> | |||
|- | |||
|<math>\psi_a(\Omega_{a+1}+\psi_a(\Omega_{a+1})\times2)</math> | |||
|<math>(1-)^{2nd~(1-)^{2nd~2}~aft~2nd~2}~aft~2nd~2</math> | |||
|<math>\Omega_2^3</math> | |||
|- | |||
|<math>\psi_a(\Omega_{a+1}+\psi_a(\Omega_{a+1}+1))</math> | |||
|<math>(1-)^{(1-)^{Ord~aft~2nd~2}~aft~2nd~2}~aft~2nd~2</math> | |||
|<math>\Omega_2^\omega</math> | |||
|- | |||
|<math>\psi_a(\Omega_{a+1}+\psi_a(\Omega_{a+1}+\psi_a(\Omega_{a+1})))</math> | |||
|<math>(1-)^{(1-)^{(1-)^{2nd~2}~aft~2nd~2}~aft~2nd~2}~aft~2nd~2</math> | |||
|<math>\Omega_2^{\Omega_2}</math> | |||
|- | |||
|<math>\psi_a(\Omega_{a+1}+a)</math> | |||
|<math>(1-)^a~aft~2</math> | |||
|<math>\psi_2(\Omega_3)</math> | |||
|- | |||
|<math>\psi_a(\Omega_{a+1}+a^a)</math> | |||
|<math>(1-)^{a^2}~aft~2</math> | |||
|<math>\psi_2(\Omega_3^{\Omega_3})</math> | |||
|- | |||
|<math>\psi_a(\Omega_{a+1}+\varepsilon_{a+1})</math> | |||
|<math>(1-)^{\varepsilon_{a+1}}~aft~2</math> | |||
|<math>\psi_2(\Omega_4)</math> | |||
|- | |||
|<math>\psi_a(\Omega_{a+1}+BO(a+1))</math> | |||
|<math>(1-)^{BO(a+1)}~aft~2</math> | |||
|<math>\psi_2(\Omega_\omega)</math> | |||
|- | |||
|<math>\psi_a(\Omega_{a+1}\times2)</math> | |||
|<math>2nd~2</math> | |||
|<math>\Omega_3</math> | |||
|- | |||
|<math>\psi_a(\Omega_{a+1}\times2+a)</math> | |||
|<math>(1-)^a~aft~2nd~2</math> | |||
|<math>\psi_3(\Omega_4)</math> | |||
|- | |||
|<math>\psi_a(\Omega_{a+1}\times3)</math> | |||
|<math>3rd~2</math> | |||
|<math>\Omega_4</math> | |||
|- | |||
|<math>\psi_a(\Omega_{a+1}\times\omega)</math> | |||
|<math>1-2</math> | |||
|<math>\Omega_\omega</math> | |||
|- | |||
|<math>\psi_a(\Omega_{a+1}\times\omega\times2)</math> | |||
|<math>2nd~1-2</math> | |||
|<math>\Omega_{\omega\times2}</math> | |||
|- | |||
|<math>\psi_a(\Omega_{a+1}\times\omega^2)</math> | |||
|<math>1-1-2</math> | |||
|<math>\Omega_{\omega^2}</math> | |||
|- | |||
|<math>\psi_a(\Omega_{a+1}\times\omega^\omega)</math> | |||
|<math>(1-)^\omega~2</math> | |||
|<math>\Omega_{\omega^\omega}</math> | |||
|- | |||
|<math>\psi_a(\Omega_{a+1}\times\psi_a(0))</math> | |||
|<math>(1-)^{(2)}~2</math> | |||
|<math>\Omega_\Omega</math> | |||
|- | |||
|<math>\psi_a(\Omega_{a+1}\times\psi_a(\Omega_{a+1}\times\omega))</math> | |||
|<math>(1-)^{1-2}~2</math> | |||
|<math>\Omega_{\Omega_\omega}</math> | |||
|- | |||
|<math>\psi_a(\Omega_{a+1}\times a)</math> | |||
|<math>(1-)^a~2</math> | |||
|<math>OFP=\psi_I(I)</math> | |||
|- | |||
|<math>\psi_a(\Omega_{a+1}\times a+\Omega_{a+1})</math> | |||
|<math>2~aft~(1-)^a~2</math> | |||
|<math>\rm \psi_I(I+1)</math> | |||
|- | |||
|<math>\psi_a(\Omega_{a+1}\times a+\Omega_{a+1}\times\psi_a(\Omega_{a+1}\times a))</math> | |||
|<math>(1-)^{(1-)^a~2}~2~aft~(1-)^a~2</math> | |||
|<math>\rm \psi_I(I+\psi_I(I))</math> | |||
|- | |||
|<math>\psi_a(\Omega_{a+1}\times a\times2)</math> | |||
|<math>2nd~(1-)^a~2</math> | |||
|<math>\rm \psi_I(I\times2)</math> | |||
|- | |||
|<math>\psi_a(\Omega_{a+1}\times a\times\omega)</math> | |||
|<math>(1-)^{a+1}~2</math> | |||
|<math>\rm \psi_I(I\times\omega)</math> | |||
|- | |||
|<math>\psi_a(\Omega_{a+1}\times a\times\psi_a(\Omega_{a+1}\times a))</math> | |||
|<math>(1-)^{a+(1-)^a~2}~2</math> | |||
|<math>\rm \psi_I(I\times\psi_I(I))</math> | |||
|- | |||
|<math>\psi_a(\Omega_{a+1}\times a^2)</math> | |||
|<math>(1-)^{a\times2}~2</math> | |||
|<math>\rm \psi_I(I^2)</math> | |||
|- | |||
|<math>\psi_a(\Omega_{a+1}\times a^3)</math> | |||
|<math>(1-)^{a\times3}~2</math> | |||
|<math>\rm \psi_I(I^3)</math> | |||
|- | |||
|<math>\psi_a(\Omega_{a+1}\times a^a)</math> | |||
|<math>(1-)^{a^2}~2</math> | |||
|<math>\rm \psi_I(I^I)</math> | |||
|- | |||
|<math>\psi_a(\Omega_{a+1}\times \varepsilon_{a+1})</math> | |||
|<math>(1-)^{\varepsilon_{a+1}}~2</math> | |||
|<math>\rm \psi_I(\Omega_{I+1})</math> | |||
|- | |||
|<math>\psi_a(\Omega_{a+1}\times BO(a+1))</math> | |||
|<math>(1-)^{BO(a+1)}~2</math> | |||
|<math>\rm \psi_I(\Omega_{I+\omega})</math> | |||
|- | |||
|<math>\psi_a(\Omega_{a+1}\times SHO(a+1))</math> | |||
|<math>(1-)^{SHO(a+1)}~2</math> | |||
|<math>\rm \psi_I(\psi_H(\varepsilon_{H+1}))</math> | |||
|- | |||
|<math>\psi_a(\Omega_{a+1}^2)</math> | |||
|<math>2~1-2</math> | |||
|<math>\rm I</math> | |||
|- | |||
|<math>\psi_a(\Omega_{a+1}^2+\Omega_{a+1})</math> | |||
|<math>2~aft~2~1-2</math> | |||
|<math>\rm \Omega_{I+1}</math> | |||
|- | |||
|<math>\psi_a(\Omega_{a+1}^2+\Omega_{a+1}\times\omega)</math> | |||
|<math>1-2~aft~2~1-2</math> | |||
|<math>\rm \Omega_{I+\omega}</math> | |||
|- | |||
|<math>\psi_a(\Omega_{a+1}^2+\Omega_{a+1}\times\psi_a(\Omega_{a+1}^2))</math> | |||
|<math>(1-)^{2~1-2}~2~aft~2~1-2</math> | |||
|<math>\rm \Omega_{I\times2}</math> | |||
|- | |||
|<math>\psi_a(\Omega_{a+1}^2+\Omega_{a+1}\times\psi_a(\Omega_{a+1}^2+1))</math> | |||
|<math>(1-)^{Ord~aft~2~1-2}~2~aft~2~1-2</math> | |||
|<math>\rm \Omega_{I\times\omega}</math> | |||
|- | |||
|<math>\psi_a(\Omega_{a+1}^2+\Omega_{a+1}\times\psi_a(\Omega_{a+1}^2+\psi_a(\Omega_{a+1}^2)))</math> | |||
|<math>(1-)^{(1-)^{2~1-2}~aft~2~1-2}~2~aft~2~1-2</math> | |||
|<math>\rm \Omega_{I^2}</math> | |||
|- | |||
|<math>\psi_a(\Omega_{a+1}^2+\Omega_{a+1}\times\psi_a(\Omega_{a+1}^2+a))</math> | |||
|<math>(1-)^{(1-)^a~aft~2~1-2}~2~aft~2~1-2</math> | |||
|<math>\rm \Omega_{\varepsilon_{I+1}}</math> | |||
|} | |} | ||
[[分类:分析]] |