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This post is more a call for people to make bounds than that I have things, though I shall try to make some bounds myself if I actually understand this. (I don't :( )

The Low Values

Vel!s work.

Rayo(10) ≥ 1.

Rayo(26) ≥ 2.

Rayo(61) ≥ 3.

Rayo(105) ≥ 4.

Exponentation

Vel!'s work

∀x,y,z: ((x, y), z) ∈ Exp ⇔ (x,y,z ∈ ω ∧ ((y = 0 ∧ z = 1) ∨ (∃a,b: Sa = y ∧ (b = zx) ∧ ((x, a), b) ∈ Exp)))
T = apply(Exp, (a, b))

Writing this without ∀ and comma's

¬(∃x:∃y:∃z:) ((x, y), z) ∈ E ⇔ (x,y,z ∈ ω ∧ ((y = 0 ∧ z = 1) ∨ (∃a:∃b: Sa = y ∧ (b = zx) ∧ ((x, a), b) ∈ E)))
T = apply(E(a, b))

What is apply here?

I hope I did this right. There are still some comma's how to eliminate them? Suprisingly, this is only 88 symbols, so is something wrong?

Can we define F(a) = E(a,a)?

How do we put a number (say, 2 or 3) in here?

How do we call this function multiple times?

I think we might be able to reach tetrational numbers with just 300 symbols.

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