投影 VS 反射稳定：修订间差异

2025年7月15日 (二) 14:03的版本

1


投影序数	反射稳定	常规表示
$ψ_{a} (0)$	$m i n 2$	$Ω$
$ψ_{a} (0) \times 2$	$(1 -)^{(2)} a f t 2$	$Ω \times 2$
$ψ_{a} (0) \times 3$	$2 n d (1 -)^{(2)} a f t 2$	$Ω \times 3$
$ψ_{a} (1)$	$(1 -)^{(2) + 1} a f t 2$	$Ω \times ω$
$ψ_{a} (2)$	$(1 -)^{(2) + 2} a f t 2$	$Ω \times ω^{2}$
$ψ_{a} (ω)$	$(1 -)^{(2) + ω} a f t 2$	$Ω \times ω^{ω}$
$ψ_{a} (B O)$	$(1 -)^{(2) + B O} a f t 2$	$Ω \times B O$
$ψ_{a} (ψ_{a} (0))$	$(1 -)^{(1 -)^{(2)} a f t 2} a f t 2$	$Ω^{2}$
$ψ_{a} (ψ_{a} (0) + 1)$	$(1 -)^{(1 -)^{(2)} a f t 2 + 1} a f t 2$	$Ω^{2} \times ω$
$ψ_{a} (ψ_{a} (0) \times 2)$	$(1 -)^{2 n d (1 -)^{(2)} a f t 2} a f t 2$	$Ω^{3}$
$ψ_{a} (ψ_{a} (1))$	$(1 -)^{(1 -)^{(2) + 1} a f t 2} a f t 2$	$Ω^{ω}$
$ψ_{a} (ψ_{a} (ψ_{a} (0)))$	$(1 -)^{(1 -)^{(1 -)^{(2)} a f t 2} a f t 2} a f t 2$	$Ω^{Ω}$
$ψ_{a} (ψ_{a} (ψ_{a} (ψ_{a} (0))))$	$(1 -)^{(1 -)^{(1 -)^{(1 -)^{(2)} a f t 2} a f t 2} a f t 2} a f t 2$	$Ω^{Ω^{Ω}}$
$ψ_{a} (a)$	$(1 -)^{a} a f t 2$	$ψ_{1} (Ω_{2})$
$ψ_{a} (a) \times 2$	$(1 -)^{(1 -)^{a} a f t 2} a f t (1 -)^{a} a f t 2$	$ψ_{1} (Ω_{2}) \times 2$
$ψ_{a} (a + 1)$	$(1 -)^{(1 -)^{a} a f t 2 + 1} a f t (1 -)^{a} a f t 2$	$ψ_{1} (Ω_{2} + 1)$
$ψ_{a} (a + ψ_{a} (a))$	$(1 -)^{(1 -)^{(1 -)^{a} a f t 2} a f t (1 -)^{a} a f t 2} a f t (1 -)^{a} a f t 2$	$ψ_{1} (Ω_{2} + ψ_{1} (Ω_{2}))$
$ψ_{a} (a \times 2)$	$2 n d (1 -)^{a} a f t 2$	$ψ_{1} (Ω_{2} \times 2)$
$ψ_{a} (a \times 3)$	$3 r d (1 -)^{a} a f t 2$	$ψ_{1} (Ω_{2} \times 3)$
$ψ_{a} (a \times ω)$	$(1 -)^{a + 1} a f t 2$	$ψ_{1} (Ω_{2} \times ω)$
$ψ_{a} (a \times ψ_{a} (a))$	$(1 -)^{a + (1 -)^{a} a f t 2} a f t 2$	$ψ_{1} (Ω_{2} \times ψ_{1} (Ω_{2}))$
$ψ_{a} (a^{2})$	$(1 -)^{a \times 2} a f t 2$	$ψ_{1} (Ω_{2}^{2})$
$ψ_{a} (a^{2} + a)$	$(1 -)^{a} a f t (1 -)^{a \times 2} a f t 2$	$ψ_{1} (Ω_{2}^{2} + Ω_{2})$
$ψ_{a} (a^{2} + a \times ψ_{a} (a^{2}))$	$(1 -)^{a + (1 -)^{a \times 2} a f t 2} a f t (1 -)^{a \times 2} a f t 2$	$ψ_{1} (Ω_{2}^{2} + Ω_{2} \times ψ_{1} (Ω_{2}^{2}))$
$ψ (a^{2} \times 2)$	$2 n d (1 -)^{a \times 2} a f t 2$	$ψ_{1} (Ω_{2}^{2} \times 2)$
$ψ (a^{2} \times ω)$	$(1 -)^{a \times 2 + 1} a f t 2$	$ψ_{1} (Ω_{2}^{2} \times ω)$
$ψ (a^{3})$	$(1 -)^{a \times 3} a f t 2$	$ψ_{1} (Ω_{2}^{3})$
$ψ_{a} (a^{ω})$	$(1 -)^{a \times ω} a f t 2$	$ψ_{1} (Ω_{2}^{ω})$
$ψ_{a} (a^{a})$	$(1 -)^{a^{2}} a f t 2$	$ψ_{1} (Ω_{2}^{Ω_{2}})$
$ψ_{a} (a^{a + 1})$	$(1 -)^{a^{2} + a} a f t 2$	$ψ_{1} (Ω_{2}^{Ω_{2} + 1})$
$ψ_{a} (a^{a + ω})$	$(1 -)^{a^{2} + a \times ω} a f t 2$	$ψ_{1} (Ω_{2}^{Ω_{2} + ω})$
$ψ_{a} (a^{a \times 2})$	$(1 -)^{a^{2} \times 2} a f t 2$	$ψ_{1} (Ω_{2}^{Ω_{2} \times 2})$
$ψ_{a} (a^{a \times ω})$	$(1 -)^{a^{2} \times ω} a f t 2$	$ψ_{1} (Ω_{2}^{Ω_{2} \times ω})$
$ψ_{a} (a^{a^{2}})$	$(1 -)^{a^{3}} a f t 2$	$ψ_{1} (Ω_{2}^{Ω_{2}^{2}})$
$ψ_{a} (a^{a^{3}})$	$(1 -)^{a^{4}} a f t 2$	$ψ_{1} (Ω_{2}^{Ω_{2}^{3}})$
$ψ_{a} (a^{a^{ω}})$	$(1 -)^{a^{ω}} a f t 2$	$ψ_{1} (Ω_{2}^{Ω_{2}^{ω}})$
$ψ_{a} (a^{a^{a}})$	$(1 -)^{a^{a}} a f t 2$	$ψ_{1} (Ω_{2}^{Ω_{2}^{Ω_{2}}})$
$ψ_{a} (ε_{a + 1})$	$(1 -)^{ε_{a + 1}} a f t 2$	$ψ_{1} (Ω_{3})$
$ψ_{a} (ζ_{a + 1})$	$(1 -)^{ζ_{a + 1}} a f t 2$	$ψ_{1} (Ω_{3}^{2})$
$ψ_{a} (Γ_{a + 1})$	$(1 -)^{Γ_{a + 1}} a f t 2$	$ψ_{1} (Ω_{3}^{Ω_{3}})$
$ψ_{a} (B H O (a + 1))$	$(1 -)^{B H O (a + 1)} a f t 2$	$ψ_{1} (Ω_{4})$
$ψ_{a} (B O (a + 1))$	$(1 -)^{B O (a + 1)} a f t 2$	$ψ_{1} (Ω_{ω})$
$ψ_{a} (Ω_{a + 1})$	$2 n d 2$	$Ω_{2}$

@@ 第1行： / 第1行： @@
 本条目展示[[投影序数]]和[[反射序数]]、[[稳定序数]]的列表分析
+=== 1 ===
 {| class="wikitable"
 |+
 !投影序数
 !反射稳定
+!常规表示
 |-
-|<math>\omega</math>
+|<math>\psi_a(0)</math>
-|<math>1</math>
+|<math>min~2</math>
+|<math>\Omega</math>
 |-
-|<math>\omega\times2</math>
+|<math>\psi_a(0)\times2</math>
-|<math>2nd~1</math>
+|<math>(1-)^{(2)}~aft~2</math>
+|<math>\Omega\times2</math>
 |-
-|<math>\omega\times3</math>
+|<math>\psi_a(0)\times3</math>
-|<math>3rd~1</math>
+|<math>2nd~(1-)^{(2)}~aft~2</math>
+|<math>\Omega\times3</math>
 |-
-|<math>\omega^2</math>
+|<math>\psi_a(1)</math>
-|<math>1-1</math>
+|<math>(1-)^{(2)+1}~aft~2</math>
+|<math>\Omega\times\omega</math>
 |-
-|<math>\omega^2+\omega</math>
+|<math>\psi_a(2)</math>
-|<math>1~aft~1-1</math>
+|<math>(1-)^{(2)+2}~aft~2</math>
+|<math>\Omega\times\omega^2</math>
 |-
-|<math>\omega^2+\omega\times2</math>
+|<math>\psi_a(\omega)</math>
-|<math>2nd~1~aft~1-1</math>
+|<math>(1-)^{(2)+\omega}~aft~2</math>
+|<math>\Omega\times\omega^\omega</math>
 |-
-|<math>\omega^2\times2</math>
+|<math>\psi_a(BO)</math>
-|<math>2nd~1-1</math>
+|<math>(1-)^{(2)+BO}~aft~2</math>
+|<math>\Omega\times BO</math>
 |-
-|<math>\omega^3</math>
+|<math>\psi_a(\psi_a(0))</math>
-|<math>1-1-1</math>
+|<math>(1-)^{(1-)^{(2)}~aft~2}~aft~2</math>
+|<math>\Omega^2</math>
 |-
-|<math>\omega^\omega</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>\omega^{\omega+1}</math>
+|<math>\psi_a(\psi_a(0)\times2)</math>
-|<math>(1-)^{\omega+1}</math>
+|<math>(1-)^{2nd~(1-)^{(2)}~aft~2}~aft~2</math>
+|<math>\Omega^3</math>
 |-
-|<math>\omega^{\omega^2}</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>\omega^{\omega^\omega}</math>
+|<math>\psi_a(\psi_a(\psi_a(0)))</math>
-|<math>(1-)^{(1-)^\omega}</math>
+|<math>(1-)^{(1-)^{(1-)^{(2)}~aft~2}~aft~2}~aft~2</math>
+|<math>\Omega^\Omega</math>
 |-
-|<math>\varepsilon_0</math>
+|<math>\psi_a(\psi_a(\psi_a(\psi_a(0))))</math>
-|<math>(1-)^a</math>
+|<math>(1-)^{(1-)^{(1-)^{(1-)^{(2)}~aft~2}~aft~2}~aft~2}~aft~2</math>
+|<math>\Omega^{\Omega^\Omega}</math>
 |-
-|<math>\varepsilon_0\times2</math>
+|<math>\psi_a(a)</math>
-|<math>(1-)^{(1-)^a}~aft~(1-)^a</math>
+|<math>(1-)^a~aft~2</math>
+|<math>\psi_1(\Omega_2)</math>
 |-
-|<math>\omega^{\varepsilon_0+1}</math>
+|<math>\psi_a(a)\times2</math>
-|<math>(1-)^{(1-)^a+1}~aft~(1-)^a</math>
+|<math>(1-)^{(1-)^a~aft~2}~aft~(1-)^a~aft~2</math>
+|<math>\psi_1(\Omega_2)\times2</math>
 |-
-|<math>\varepsilon_1</math>
+|<math>\psi_a(a+1)</math>
-|<math>2nd~(1-)^a</math>
+|<math>(1-)^{(1-)^a~aft~2+1}~aft~(1-)^a~aft~2</math>
+|<math>\psi_1(\Omega_2+1)</math>
 |-
-|<math>\varepsilon_\omega</math>
+|<math>\psi_a(a+\psi_a(a))</math>
-|<math>(1-)^{a+1}</math>
+|<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>\varepsilon_{\varepsilon_0}</math>
+|<math>\psi_a(a\times2)</math>
-|<math>(1-)^{a+(1-)^a}</math>
+|<math>2nd~(1-)^a~aft~2</math>
+|<math>\psi_1(\Omega_2\times2)</math>
 |-
-|<math>\zeta_0</math>
+|<math>\psi_a(a\times3)</math>
-|<math>(1-)^{a\times2}</math>
+|<math>3rd~(1-)^a~aft~2</math>
+|<math>\psi_1(\Omega_2\times3)</math>
 |-
-|<math>\varphi(\omega,0)</math>
+|<math>\psi_a(a\times\omega)</math>
-|<math>(1-)^{a\times\omega}</math>
+|<math>(1-)^{a+1}~aft~2</math>
+|<math>\psi_1(\Omega_2\times\omega)</math>
 |-
-|<math>\psi(\Omega^\Omega)</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>\psi(\Omega^{\Omega\times2})</math>
+|<math>\psi_a(a^2)</math>
-|<math>(1-)^{a^2\times2}</math>
+|<math>(1-)^{a\times2}~aft~2</math>
+|<math>\psi_1(\Omega_2^2)</math>
 |-
-|<math>\psi(\Omega^{\Omega^2})</math>
+|<math>\psi_a(a^2+a)</math>
-|<math>(1-)^{a^3}</math>
+|<math>(1-)^a~aft~(1-)^{a\times2}~aft~2</math>
+|<math>\psi_1(\Omega_2^2+\Omega_2)</math>
 |-
-|<math>\psi(\Omega^{\Omega^\omega})</math>
+|<math>\psi_a(a^2+a\times\psi_a(a^2))</math>
-|<math>(1-)^{a^\omega}</math>
+|<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>\psi(\Omega^{\Omega^\Omega})</math>
+|<math>\psi(a^2\times2)</math>
-|<math>(1-)^{a^a}</math>
+|<math>2nd~(1-)^{a\times2}~aft~2</math>
+|<math>\psi_1(\Omega_2^2\times2)</math>
 |-
-|<math>\psi(\Omega_2)</math>
+|<math>\psi(a^2\times\omega)</math>
-|<math>(1-)^{\psi_{\Omega_{a+1}}(\Omega_{a+1})}</math>
+|<math>(1-)^{a\times2+1}~aft~2</math>
+|<math>\psi_1(\Omega_2^2\times\omega)</math>
 |-
-|<math>\psi(\Omega_2^2)</math>
+|<math>\psi(a^3)</math>
-|<math>(1-)^{\psi_{\Omega_{a+1}}(\Omega_{a+1}^2)}</math>
+|<math>(1-)^{a\times3}~aft~2</math>
+|<math>\psi_1(\Omega_2^3)</math>
 |-
-|
+|<math>\psi_a(a^\omega)</math>
-|<math>(1-)^{\psi_{\Omega_{a+1}}(\Omega_{a+1}^a)}</math>
+|<math>(1-)^{a\times\omega}~aft~2</math>
+|<math>\psi_1(\Omega_2^\omega)</math>
 |-
-|
+|<math>\psi_a(a^a)</math>
-|<math>(1-)^{\psi_{\Omega_{a+1}}(\Omega_{a+1}^{\Omega_{a+1}})}</math>
+|<math>(1-)^{a^2}~aft~2</math>
+|<math>\psi_1(\Omega_2^{\Omega_2})</math>
 |-
-|
+|<math>\psi_a(a^{a+1})</math>
-|<math>(1-)^{\psi_{\Omega_{a+1}}(\Omega_{a+2})}</math>
+|<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-)^{\psi_{\Omega_{a+1}}(\Omega_{a+\omega})}</math>
+|<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>
 |}
+[[分类:分析]]