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arXiv · 2507.01760

Dimension theory for the asymptotic couple of the field of logarithmic transseries

Allen Gehret·Elliot Kaplan·Nigel Pynn-Coates
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Abstract

In this paper we completely characterize all dimension functions on all models of the theory $T_{\log}$ of the asymptotic couple of the field of logarithmic transseries (Dimension Theorem). This is done by characterizing the "small" $1$-variable definable sets (Small Sets Theorem). As a byproduct, we show that $T_{\log}$ is d-minimal and does not eliminate imaginaries. Separately, we provide an abstract criterion for d-minimality, which we use to observe some new examples of d-minimal expansions of valued fields.

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Allen Gehret, Elliot Kaplan, Nigel Pynn-Coates. 2025-07-02. Dimension theory for the asymptotic couple of the field of logarithmic transseries. https://arxiv.org/abs/2507.01760

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