User blog comment:Hyp cos/TON, stable ordinals, and my array notation/@comment-31580368-20191006023842/@comment-31580368-20191009014236

Hyp cos found several gaps in my analysis of gaps-ordinals (gaps in gaps =) ). Also, I myself noticed several errors in comparison with TON. Here are the comparisons that were wrong:

C(&Omega;2+C(&Omega;2&times;&omega;2,0),0) - start 1st 2nd-order gap length &omega;; 1st &beta;|(L&beta;/L&beta;+2)&cap;P(&omega;)=&empty;; &beta;|L&beta;⊧П21-CA0

C(&Omega;2+C(&Omega;2&times;C(&Omega;2+C(&Omega;2&times;2+1,0),0),0),0) - 1st limit of &beta;=(start 1st 2nd-order gap length (n&lt;&omega;)-ple stable after &beta;);

C(&Omega;2+C(&Omega;2&times;C(&Omega;2+C(&Omega;2&times;&omega;,0),0),0),0) - start 1st 2nd-order gap length &beta;=(1st 2nd-order-gap with length &quot;next 2nd-order gap ordinal after &beta;&quot;);

C(&Omega;2+C(&Omega;2&times;C(&Omega;2&times;2,0),0),0) -1st limit of &beta;&lt;&alpha;|(L&beta;/L&alpha;)&cap;P(&omega;)=&empty;; nonprojectable 2nd-order gap; &beta;|L&beta;⊧П22-CA0

C(&Omega;2+C(&Omega;2&times;C(&Omega;2&times;&omega;,0),0),0) - start 1st 3d-order gap length 1; 1st &beta;|(L&beta;/L&beta;+1)&cap;P(P(&omega;))=&empty;; &beta;|L&beta;⊧Z3; &beta;|L&beta;⊧ZFC-+&exist;P(&omega;)