Distality for the Asymptotic Couple of the Field of Logarithmic Transseries

Allen Gehret; Elliot Kaplan

doi:10.1215/00294527-2020-0010

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 (have the non-independence property), this provides a new proof that $T_{\log }$ is NIP.

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Allen Gehret. Elliot Kaplan. "Distality for the Asymptotic Couple of the Field of Logarithmic Transseries." Notre Dame J. Formal Logic 61 (2) 341 - 361, May 2020. https://doi.org/10.1215/00294527-2020-0010

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Received: 22 May 2018; Accepted: 8 December 2019; Published: May 2020

First available in Project Euclid: 7 April 2020

zbMATH: 07222695

MathSciNet: MR4092539

Digital Object Identifier: 10.1215/00294527-2020-0010

Subjects:

Primary: 03C64

Secondary: 03C45 , 06F20

Keywords: asymptotic couples , asymptotic integration , distality , dp-rank , independence property , indiscernible sequences , logarithmic transseries

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