Up-arrow notation level

This category contains numbers that can be defined or estimated using up-arrow notation, which is equivalent to Jonathan Bowers' 3-entrical arrays. The first numbers that has to be expressed using nonprimitive recursive functions, such as the Ackermann function, resides here.

The lower bound of this category is \(10 \uparrow\uparrow\uparrow 3 = 10 \uparrow\uparrow 10 \uparrow\uparrow 10\), and the upper bound is \(f_\omega(f_3(10))\).