User blog comment:Nayuta Ito/What We've Agreed on Stage Cardinal/@comment-11227630-20180522030604/@comment-11227630-20180525142137

Stage cardinals haven't a well definition yet. What I wrote here is a corresponding with Taranovsky's ordinal notation, which works well with the concepts of uncountable regular cardinals, inaccessibles, Mahlos and the weakly compact.

Definition of my version of stage cardinals:
 * 1) C(Ω2+f(t)) = S(ωf(T)) where t = C(Ω2,C(Ω22,0))
 * 2) C(Ω2+α1,...C(Ω2+αn,0)...) = S(β1+...+βn) if C(Ω2+αi,0) = S(βi) for all i