User blog comment:Moooosey/Simple psi-- a fairly simple ocf/@comment-43798125-20191026225036/@comment-39541634-20191027153227

"What would happen if you allowed powers and multiplication, and also added W_2 to the initial set? Not that I didn't read your comment and how you add operations, not more ordinals in the initial set, I'm just curious."

A very similar thing to the example I've already shown you.

You'll have ψ(Ω2)=BHO

And the limit of the new system would be ψ(Ω2^Ω2^Ω2^...). We could then add Ω3 and continue from there. Then ψ(Ω3^Ω3^Ω3^...)=ψ(Ω4) and so on.

Here's something interesting I just realized:

Every new ad-hoc addition you make to the initial set, is equivalent to incrementing the argument of a second OCF by 1.

You're probably asking yourself what the bleep does that mean. An example will make it clear:

In the system you proposed just now, ψ(Ω2)=BHO. In a standard multiple-OCF system, this would be written as ψ(ψ1(0)).

ψ(Ω3) in your proposed system corresponds to ψ(ψ1(1)) in a standard multiple-OCF system.

ψ(Ω4) in your proposed system corresponds to ψ(ψ1(2)).

ψ(Ω5) in your proposed system corresponds to ψ(ψ1(3)).

See the pattern? When we add a second OCF as a "generator function", it generates the ordinals you need to get unstuck on the fly! One new ordinal per entry. It's a dream come true! The closest thing to a "magic bullet" that you can get... at least until you run out of indexes to feed ψ1 (which happens at ψ(ψ1(ψ1(ψ1(...))))).

As for the rest of your questions:

I really recommend that you try to work those answers out yourself. There's only so much you can learn merely by reading what other people are doing. Trying to analyze examples yourself is the best way to learn these things.