Liouville closure?
Since $\K$ is not closed under exponentiation, it is fair to ask whether the Liouville closure of $\K$ is again an Ilyashenko field. This appears to be the case; indeed, working with Margaret Thomas, we conjecture that if $(\la, \M, T)$ is any Ilyashenko field with $\M$ the set of (not necessarily convergent) LE-monomials, then…