Moving along, I'm not that big of a fan of unnamed numbers, so here is a table of the numbers I have dubbed/nicknamed:
My nickname
Definition
Notes
Madore's ordinal
Collapse of , where refers to the first inaccessible
PTO of KPi, - CA + BI
Small Rathjen ordinal
, where refers to the first Mahlo, using Rathjen's psi function
PTO of KPM, designated ϑ by Rathjen
Large Rathjen ordinal
, where refers to the first weakly compact, using Rathjen's Psi function
PTO of KP + - Ref
Small Stegert ordinal
, where refers to the first -indescribable and = (; ; , , 0)
PTO of KP + - Ref
Large Stegert ordinal
, where = (; ; , , 0)
PTO of Stability
Great Church-Kleene ordinal
The smallest limit of admissibles. This ordinal is not admissible. An extension of the Church-Kleene ordinal.
Devlin-Jech ordinal
The smallest ordinal such that
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