## Ilyashenko algebras based on definable monomials, revisited

In order to address some of the questions raised in this post, I introduce here some relevant definitions and recast the construction of Ilyashenko algebras based on $\log$ monomials using these new notions. As before, let $\H$ be the Hardy field of germs at $+\infty$ of all $h:\RR \into \RR$ definable in $\Ranexp$, and denote…