H-fields and their Liouville extensions

Matthias Aschenbrenner; Lou Van Den Dries

doi:10.1007/s002090000358

H-fields and their Liouville extensions

Matthias Aschenbrenner
, Lou Van Den Dries

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We introduce H-fields as ordered differential fields of a certain kind. Hardy fields extending as well as the field of logarithmic-exponential series over are H-fields. We study Liouville extensions in the category of H-fields as a step towards a model theory of H-fields. The main result is that an H-field has at most two Liouville closures.

Original language	English (US)
Pages (from-to)	543-588
Number of pages	46
Journal	Mathematische Zeitschrift
Volume	242
Issue number	3
DOIs	https://doi.org/10.1007/s002090000358
State	Published - 2002

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General Mathematics

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10.1007/s002090000358

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abstract = "We introduce H-fields as ordered differential fields of a certain kind. Hardy fields extending as well as the field of logarithmic-exponential series over are H-fields. We study Liouville extensions in the category of H-fields as a step towards a model theory of H-fields. The main result is that an H-field has at most two Liouville closures.",

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AU - Aschenbrenner, Matthias

AU - Van Den Dries, Lou

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AB - We introduce H-fields as ordered differential fields of a certain kind. Hardy fields extending as well as the field of logarithmic-exponential series over are H-fields. We study Liouville extensions in the category of H-fields as a step towards a model theory of H-fields. The main result is that an H-field has at most two Liouville closures.

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H-fields and their Liouville extensions

Abstract

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