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Analytic Hardy fields

delete2026-04-01
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PRE
AI
M
Matthias Aschenbrenner *
V
van den Dries, Lou
DOI:10.1017/s0010437x26102929delete
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Abstract

Abstract

En 中文
We show that maximal analytic Hardy fields are $\eta_1$ in the sense of Hausdorff. We also prove various embedding theorems about analytic Hardy fields. For example, the ordered differential field $ {\mathbb T} $ of transseries is shown to be isomorphic to an analytic Hardy field.
Keywords:
Hardy fields
transseries
Whitney approximation theorem

Journal

C
Compositio Mathematica
IF:
1.4
Papers:
46
Citations:
0

Organization

U
university of vienna
Scholars:
2.9K
Papers: 1.5K
Citations: 0
University of Illinois System cover
University of Illinois System
Scholars:
6.9W
Papers: 6.2W
Citations: 644
Cited Papers

Cited Papers

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Maximal immediate extensions of valued differential fields
err2018-08-01
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PREAI
errAschenbrenner,Matthias; van den Dries,Lou; van der Hoeven,Joris
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The surreal numbers as a universal $H$-field
err2019-01-07
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PREAI
errAschenbrenner,Matthias; van den Dries,Lou; van der Hoeven,Joris
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Logarithmic-exponential series
err2001-07-01
err0
PREAI
errvan den Dries,Lou; Macintyre,Angus; Marker,David
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