User blog comment:Pellucidar12/Attempt at a FGH related notation/@comment-29915175-20170416151157/@comment-30754445-20170418170830

"Is there a page somewhere that shows all of the different FS that have been defined"

ALL of them? Probably not.

But you can find some fundamental sequences in:

1. Deedlit's blog series (6 parts) about ordinal notation.

2. A few blog posts by Denis Maksudov whose sole purpose was to define FS up to certain ordinals.

3. My own blog post titled "Formal Definition of Letter Notation Up To R For Integer Arguments" (which goes only up to Γ₀ - for now).

Note that none of these get all the way up to ωck. It is impossible - in principle - to explicitly write down the rules for all fundamental sequences up to ωck. No set of rules... no algorithm can do the job. That's precisely what the phrase "ωck is uncomputable" means.

At any rate, I strongly recommend that you try to create your own FS and rules, using the above references only as a guideline. You'll learn much faster that way.