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 $\mathrm{dp}$-minimal and it does not have finite $\mathrm{dp}$-rank.

arXiv comment16 pp; 3 figures

References in corpus (2)

• Distal and non-distal NIP theories
• A tale of two Liouville closures