User blog comment:Scorcher007/Large countable ordinal notation up to Z2 and ZFC/@comment-11227630-20190803082138/@comment-31580368-20190803094853

According to M. Srebrny 1973 β0 (1st start 1st 2nd-order gap length 1) is (+1)-stable, but not (+2)-stable. Then we can define (+2)-stable after β0, ... 2-(+2)-stable after β0..., and finally β1 (2nd start 1st 2nd-order gap length 1).

Then you can act in a similar way like: "П2-(St)-reflecting, where St is set of stable below, П3-(St)-reflecting, and finally (+1)-2-stable".

П2-(Gp)-reflecting, where Gp is set of gap ordinal below, П3-(Gp)-reflecting, and finally Пω-(Gp)-reflecting. I called it start "start 1st 2nd-order gap length 1 and (+1)-2-stable"

"start 1st 2nd-order gap length 1 and (+2)-ω-stable" should be start 1st 2nd-order gap length 2.