The Arias Function: An Iteration of the Rayo Operator in a Second-Order Language

We introduce a function of extreme growth defined by iterating the Rayo operator in a second-order formal language. Although the function was constructed independently, its analysis reveals that its canonical form corresponds to a functional iteration of Rayo₂. A conceptual interpretation of this function as an iteration of the principle of maximal definability is discussed, and a concrete value, called the Arias number, is introduced as a reference of its magnitude.