The theory of maximal Hardy fields

2024/08/02 by Aschenbrenner, Matthias, Dries, Lou van den, van der Hoeven, Joris · 2 citations
#Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2408.05232

Abstract

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

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• Maximal Hardy Fields
• Hardy fields, the intermediate value property, and ω-freeness
• Analytic Hardy fields
• Relative differential closure in Hardy fields
• Constant power maps on Hardy fields and transseries