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arXiv · 1802.05732

Distality for the asymptotic couple of the field of logarithmic transseries

Allen Gehret·Elliot Kaplan
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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.

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Allen Gehret, Elliot Kaplan. 2018-02-15. Distality for the asymptotic couple of the field of logarithmic transseries. https://doi.org/10.1215/00294527-2020-0010

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