User blog comment:Boboris02/Algorithm for Generating LUCOs From TON Expressions + Intuitive Analysis/@comment-31580368-20180519034242

As I understand:

Nonprojectible Ordinals analisys - means, up to Z2 or ZFC-

Fully Stable Ordinals analisys - means up to ZFC

included:

KP+ω1

Z3 or ZFC-+ω1

KP+ω2

Z4 or ZFC-+ω2

ZFC-+ωω

ZFC-+ω-1st fixed point

e.t.c. up to ZFC