This function is much larger than I've ever made. It contains ExE, BEAF, and other extensions.


M Ax{0}y=M Ax-1{0}(M Ax{0}y-1)
M Ax{0}y{0}0 B= M Ax{0}y-1{0}y B

The notation of this level is not so important. Any linear function is OK. So, if this definition is ill-defined, use BEAF instead.

Next, there comes ExE.

K is some brackets.
M xK{0}y = MxKxK...Kx (y x's)
M xK{n}y = MxK{n-1}xK{n-1}...K{n-1}x (y x's)
M A x{a}^{0}y =M A x{a}{a}...{a}x (y {0}'s)
M A x{a}^{n}y =M A x{a}^{n-1}x{a}^{n-1}...x{a}^{n-1}x (y {0}'s)

I don't know how to write, but the same thing as # and ^ in ExE happens. I think it's already f_{\omega^{\omega^{\omega}}}(x).


Mx{1}y=Mx{0}^^...^^{0}x (y ^'s)

Then, we can define x{1}{0}y, x{1}{1}y, and so on.

Mx{n}y=Mx{n-1}^^...^^{n-1}x (y ^'s)

The {n} means "level-n #" in ExE.

I think it will be up to f_{\epsilon_0}(x).

(Next: Something like x{1,0}y)

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