User blog comment:Scorcher007/Large countable ordinal notation up to Z2 and ZFC/@comment-11227630-20190803082138/@comment-31580368-20190803120140

I noticed that from now on, the end of the gap ordinal behaves similar to the concept of stability, and obviously it can be continued to the limit of ZFC. I have displayed this relationship in this notation. S-expressions is admissible ordinals and limit of admisible ordinals including stable ordinals up limit Z2 (β|(Lβ/Lβ+1)∩ω1=∅). G-expressions is gap ordinals and so far unknown to me extension for ordinals like height model ZFC-+"ωω 1 exists" up limit ZFC (ZFC-+"β|(Vβ/Vβ+1)∩Vγ=∅). The notation can be continued: I1-expressions is large countable ordinals up limit ZFC+inaccessible cardinal (ZFC-+"β|(Vβ/Vβ+1)∩Vγ+ω=∅(where γ - inaccessible cardinal) exists"), I2-expressions is large countable ordinal up limit ZFC+2-inaccessible cardinal (ZFC-+"β|(Vβ/Vβ+1)∩Vγ+ω=∅(where γ - 2-inaccessible cardinal) exists"), e.t.c.