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This is a Quantitative Study study.

October 16, 2025Open Access

Short Hardy fields

Key Points

Differentially algebraic extensions of short hardy fields are confirmed to be short as well, reinforcing earlier studies.
The result extends Rosenlicht's theorem by establishing isomorphism in asymptotic couples of hardy type.
The analysis is set in the broader context of H-fields, enhancing the relevance of the findings.
Connections to analytic hardy fields offer new insights into the structure of short asymptotic couples.

Abstract

Differentially algebraic Hardy field extensions of short Hardy fields are short. This is proved in the more general setting of H-fields. As an application we extend a theorem of Rosenlicht (1981) by showing that each short asymptotic couple of Hardy type with small derivation is isomorphic to the asymptotic couple of an analytic Hardy field.

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Cite This Study

Aschenbrenner et al. (Fri,) studied this question.

synapsesocial.com/papers/68f12bfb2107091eab27a24a https://doi.org/https://doi.org/10.48550/arxiv.2508.06161

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