User blog comment:Rgetar/Ordinal Explorer Online/@comment-31040770-20200217035813/@comment-32213734-20200217053841

Yes, I already have seen it yesterday.

I'm going to make up a designation for "next ordinal of given family of ordinals above given ordinal α", something like
 * ε• ↰ α (for next ε number above α)
 * φ(1, 0, •) ↰ α = Γ• ↰ α (for next Γ number above α)
 * Ω• ↰ α (for next Ω number above α)
 * Φ(1, •) ↰ α
 * Φ(2, •) ↰ α
 * Φ(1, 0, •) ↰ α
 * Φ(1, 1, •) ↰ α
 * Φ(1, •, 0) ↰ α
 * I• ↰ α (for next weakly inaccessible above α)
 * I(2, •) ↰ α
 * I(1, 0, •) ↰ α
 * I(1, •, 0) ↰ α
 * etc.

Or, maybe, I'll use another symbol instead of "↰". I am going to write a blog about it, and I hope that it can help to explain how booster-base system works.

And yes, I is the least inaccessible (currently I have no I2, I3, ... I(2, 0), ...), but I plan to add them, as well as other more readable designations. I think that [L] = [Φ(1, 0)], and [L + I] = [Φ(1, 0)2], where Φ(1, 0) is limit of Ω, ΩΩ, ΩΩ Ω, ...