We show that all maximal Hardy fields are elementarily equivalent as differential fields to the differential field T of transseries, and give various applications of this result and its proof.

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

synapsesocial.com/papers/68e55b65e2b3180350ef914a https://doi.org/https://doi.org/10.48550/arxiv.2408.05232

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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

1Filling gaps in Hardy fields2024
2Short Hardy fields2025
3Tame pairs of transseries fields2024
4Normalizing Asymptotic Differential Equations2024 · 1 citations
5A Differential-Algebraic Closure Framework for Hilbert's 12th Problem:A Unified Approach to Explicit Class Field Theory2025