User blog comment:Scorcher007/Hierarchy of ordinals Z 2. Help me to understand/@comment-25601061-20180825031717/@comment-31580368-20180825073806

And here I compiled a hierarchy of subsystems Z2. Correct me where I&#39;m wrong.

&omega;&omega;undefined~ П00-CA0 ; &Delta;01-CA0 ; RCA0

&epsilon;0~ П10-CA0 ; &Delta;11-CA0 ; ACA0

&epsilon;&epsilon; 0 ~ П10-CA ; ACA

&phi;(&epsilon;0,0) ~ &Delta;11-CA

&phi;(1,0,0) ~ П10-TR0 ; ATR0

&phi;(1,0,&epsilon;0) ~ П10-TR ; ATR

&phi;(1,&omega;,0) ~ &Delta;11-TR0

&phi;(1,&epsilon;0,0) ~ &Delta;11-TR

&psi;(&epsilon;&Omega;+1) ~ П10-CA+BI ; ACA+BI

&psi;(&phi;(&epsilon;&Omega;+1,0)) ~ &Delta;11-CA+BI

&psi;(Г&Omega;+1) ~ П10-TR+BI

&psi;(&phi;(1,&Omega;+1,0)) ~ &Delta;11-TR+BI

&psi;(&Omega;&omega;) ~ П11-CA0 ; &Delta;12-CA0

&psi;(&Omega;&omega;&times;&epsilon;0) ~ П11-CA

&psi;(&epsilon;&Omega; &omega;+1 ) ~ П11-CA+BI

&psi;(&Omega;&epsilon; 0 ) ~ &Delta;12-CA

&psi;(&psi;I(0)) ~ П11-TR0

&psi;(&psi;I(0)&times;&epsilon;0) ~ П11-TR

&psi;(&epsilon;&psi; I(0)+1 ) ~ П11-TR+BI

&psi;(I&omega;) ~ &Delta;12-TR0

&psi;(I&epsilon;0) ~ &Delta;12-TR

&psi;(&epsilon;I+1) ~ &Delta;12-CA+BI

&psi;(&psi;I 2 (0)) ~ &Delta;12-TR+BI

&psi;(&omega;-leundefinedstable) = &psi;(nonprojectible) ~ П12-CA0 ; &Delta;13-CA0

&psi;(&omega;+1-le (&epsilon;a+1)-stable) ~ П12-CA ???

&psi;(&omega;+1-le stable) ~ П12-CA+BI

&psi;(&epsilon;0-le stable) ~ &Delta;13-CA

&psi;(&alpha;-le stable) ~ П12-TR0 ???

&psi;(&alpha;-le (&epsilon;a+1)-stable) ~ П12-TR ???

&psi;(&alpha;+1-le stable) ~ П12-TR+BI ???

&psi;(&alpha;-le stable with (&omega;,0)-fixed point of &alpha;) ~ &Delta;13-TR0 ???

&psi;(&alpha;-le stable with (&epsilon;0,0)-fixed point of &alpha;) ~ &Delta;13-TR ???

&psi;(1st inaccessibility of &alpha;-le stable) ~ &Delta;13-CA+BI ???

&psi;(2nd inaccessibility of &alpha;-le stable) ~ &Delta;13-TR+BI ???

&psi;((a+1)+stablity of &alpha;-le stable) = &psi;(2-(a+1)-stable) = &psi;(La≺2La+1) ???

&psi;(doubly 2-(a+1)-stable) = &psi;(La≺2Lb≺2Lb+1)

&psi;(&omega;-leundefined2-stable) ~ П13-CA0 ; &Delta;14-CA0

&psi;(&omega;-leundefined3-stable) ~ П14-CA0 ; &Delta;15-CA0

&psi;(&omega;-stable) ~ Z2