In this talk, we will prove that given any generalized analytic function, defined in a neighbourhood of the origin in the non-negative orthant of the three-dimensional Euclidean space, it is always possible to transform it into a generically monomial one (with respect to the generalized-analytic components) by means of a finite sequence of global blowing-ups.

To this end, first of all, we will recall the basics of formal generalized power series, following the previous work carried out by P. Speissegger and L. van den Dries on generalized analytic functions, as well as the paper of R. Martín-Villaverde, F. Sanz Sánchez and J.-P. Rolin where they first introduced the category of generalized analytic manifolds, gave a suitable definition of blowing-ups and proved the local monomialization of generalized analytic functions. Once this is done, we will prove the announced monomialization statement. We will use linear algebra methods to deal with and solve the combinatorial and geometric difficulties behind this problem, which will allow us to set out a global monomialization algorithm that ensures the desired result.