Ilyashenko algebras: putting it all together

Let $f = (f_0, \dots, f_k)$ be such that each $f_i \in \H$ is infinitely increasing and $f_0 \gt \cdots \gt f_k$. To see what it takes to generalize our construction of the Ilyashenko algebra $(\F,L,T)$ to more general monomials $f$, recall the construction in the following schematic:  \begin{matrix} \RR & \xrightarrow{\text{(UP)}} & \begin{bmatrix}…