Distality for the asymptotic couple of the field of logarithmic transseries

Abstract

We show that the theory $T_{\log}$ of the asymptotic couple of the field of logarithmic transseries is distal. As distal theories are NIP (= the non-independence property), this provides a new proof that $T_{\log}$ is NIP. Finally, we show that $T_{\log}$ is not strongly dependent, and in particular, it is not $\operatorname{dp}$-minimal and it does not have finite $\operatorname{dp}$-rank.