Short Hardy fields
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908482352971776 |
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| author | Aschenbrenner, Matthias Dries, Lou van den |
| author_facet | Aschenbrenner, Matthias Dries, Lou van den |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_06161 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Short Hardy fields Aschenbrenner, Matthias Dries, Lou van den Logic Commutative Algebra Classical Analysis and ODEs Number Theory 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. |
| title | Short Hardy fields |
| topic | Logic Commutative Algebra Classical Analysis and ODEs Number Theory |
| url | https://arxiv.org/abs/2508.06161 |