User blog:Scorcher007/Hierarchy of ordinals Z 2. Help me to understand

Help those who understand the hierarchy of ordinals to the level of Z2. Have I built the list of ordinals correctly?

(zoooo #) means number of ordinals in Madore's Zoo of ordinals

 countable ordinal ~ '''equiv. cardinal ~ PTO'''

1&bull; &omega;1CK = 1st admissible = П10-comprehension = (zoooo 2.1) ~ &omega;1 = 1st uncountable = 1st 1-regular ~ OCF&rarr;PTO ACA0

2&bull; &omega;2CK = 2nd admissible ~ &omega;2 = 2nd uncountable = 2nd 1-regular ~ OCF&rarr;KP&omega;

3&bull; &omega;&omega;CK = &omega;-th admissible = П11-comprehension = (zoooo 2.2) ~ &omega;&omega; = &omega;-th uncountable = &omega;-th 1-regular ~ OCF&rarr;PTO П11-CA0

4&bull; I ~ recursively inaccessible ~ weakly inaccessible = (zoooo 2.3) ~ OCF&rarr;PTO KPi

5&bull; M ~ recursively Mahlo ~ weakly Mahlo = (zoooo 2.5) ~ OCF&rarr;PTO KPM

6&bull; K ~ П3-reflection = 2-admissible = (zoooo 2.6) ~ П11-indescribable = 2-regular = weakly copmact ~ OCF&rarr;PTO KP+П3

7&bull; П4-reflection = 3-admissible ~ П12-indescribable = 3-regular ~ OCF&rarr;PTO KP+П4

8&bull; Пn+2-reflection = n+1-admissible ~ П1n-indescribable = n+1-regular ~ OCF&rarr;PTO KP+Пn+2

9&bull; П&omega;-reflection = П10-reflection = &omega;-admissible = (a+1)-stable = La≺1La+1 = (zoooo 2.7) ~ 1-П10-indescribable = 1-indescribable = П20-indescribable ;= &omega;-regular ~ OCF&rarr;PTO KP+П&omega;

10&bull; П3-reflection on (a+1)-stable ~ 1-П11-indescribable = П21-indescribable

11&bull; П4-reflection on (a+1)-stable ~ 1-П12-indescribable = П22-indescribable

12&bull; (a+2)-stable = La≺1La+2 ~ 2-П10-indescribable = 2-indescribable = П30-indescribable

13&bull; (a+n)-stable = La≺1La+n ~ n-П10-indescribable = n-indescribable = Пn+10-indescribable

14&bull; (a+&omega;)-stable = La≺1La+&omega; ~ &omega;-indescribable = total indescribable

15&bull; (a+&epsilon;0)-stable = La≺1La+&epsilon; 0 ~ &epsilon;0-indescribable

16&bull; (a+&omega;1CK)-stable = La≺1La+&omega; 1CK ~ &omega;1-indescribable

17&bull; (a+I)-stable = La≺1La+I ~ I-indescribable

18&bull; (a+M)-stable = La≺1La+M ~ M-indescribable

19&bull; (a+(b+1)-stable)-stable = La≺1La+L b≺Lb+1 ~ 1-indescribable-indescribable

20&bull; (a+(b+(c+1)-stable)-stable)-stable = La≺1La+L b≺Lb+L c≺Lc+1 ~ 1-indescribable-indescribable-indescribable

21&bull; &alpha;↦(a+&alpha;)-stable = &alpha;↦La≺1La+&alpha; ~ &alpha;↦&alpha;-indescribable (1st fixed point)

22&bull; (a+&alpha;/2)-stable = &alpha;↦La≺1La+&alpha; /2 ~ &alpha;/2-indescribable (2nd fixed point)

23&bull; &upsih; ~ (a&times;2)-stable = La≺1La&times;2 ~ subtle ~ OCF&rarr;PTO KPi+&forall;n&exist;a&ge;n(La≺1La+n)

24&bull; (a2)-stable = La≺1La2

25&bull; (aa)-stable = La≺1Laa

26&bull; (&epsilon;a+1)-stable = La≺1L&epsilon; a+1

27&bull; (+)-stable = (zoooo 2.8) = La≺1L&omega; a+1CK

28&bull; (++)-stable = (zoooo 2.10) = La≺1L&omega; a+2CK

29&bull; inaccessibly-stable = (zoooo 2.11) = La≺1LI a+1

30&bull; Mahlo-stable = (zoooo 2.12) = La≺1LM a+1

31&bull; doubly (a+1)-stable = (zoooo 2.13) = La≺1Lb≺1Lb+1

32&bull; triple (a+1)-stable = La≺1Lb≺1Lс≺1Lс+1

33&bull; &omega;-le (a+1)-stable = &alpha;↦La≺1&alpha; (1st fixed point)

34&bull; &omega;&times;2-le (a+1)-stable = La≺1&alpha;/2 (2nd fixed point)

35&bull; &Sigma;1-admissible = nonprojectible = La≺1Lb is unbounded in a,undefinedb&lt;a = П12-comprehension = (zoooo 2.15) ~ OCF&rarr;PTO П12-CA0

36&bull; 2-(a+1)-stable = La≺2La+1

37&bull; &Sigma;2-admissible = La≺2Lb is unbounded in a,undefinedb&lt;a = П13-comprehension ~ OCF&rarr;PTO П13-CA0

38&bull; 3-(a+1)-stable = La≺3La+1

39&bull; &Sigma;3-admissible = La≺3Lb is unbounded in a,undefinedb&lt;a = П14-comprehension ~ OCF&rarr;PTO П14-CA0

40&bull; &Sigma;&omega;-admissible = П1&omega;-comprehension = &beta;0 = (zoooo 2.17) ~ OCF&rarr;PTO Z2

And two important questions.

1) Does &alpha;↦&alpha;-indescribable (21&bull;) exist? There is no &kappa; which is &kappa;-indescribable (http://cantorsattic.info/Indescribable), but (21&bull;) similar to this definition. What about (22&bull;) &alpha;↦&alpha;-indescribable (2nd fixed point). Or maybe (21&bull;) = (23&bull;)?

2) Does &omega;-le stable (33&bull;) exist? And what about (34&bull;), does it make sense?