User blog comment:Scorcher007/S - Large Countable Ordinal Notation. Chapter I, Up to KPm./@comment-31580368-20190912145823/@comment-31580368-20190916004402

Well, while I do not know how to solve this problem, I will remove the Θ-function from the definition.

Let the comparison table mean the following: Limit estimation for creating any system of fundamental sequences associated with OCF based on this ordinal or collection of ordinals.

> Please remember that admissible ordinals are recursive analogues of cardinals, but are not recursive.

Actually, large cardinals and large countable ordinals are not exactly analogs. In fact, the hierarchy of cardinals is much richer (especially if we mean strong inaccessibility). For example, we can define such cardinals: power-admissible (admissible on fixed point of α↦ωα) Σn-extendible (β|Vβ≺nVγ, where γ - inaccessible cardinal, n∈N, n>1) greatly Mahlo e t.c.