Relative differential closure in Hardy fields
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914503925432320 |
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| author | Aschenbrenner, Matthias Dries, Lou van den van der Hoeven, Joris |
| author_facet | Aschenbrenner, Matthias Dries, Lou van den van der Hoeven, Joris |
| contents | We study relative differential closure in the context of Hardy fields. Using our earlier work on algebraic differential equations over Hardy fields, this leads to a proof of a conjecture of Boshernitzan (1981): the intersection of all maximal analytic Hardy fields agrees with that of all maximal Hardy fields. We also generalize a key ingredient in the proof, and describe a cautionary example delineating the boundaries of its applicability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_10764 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Relative differential closure in Hardy fields Aschenbrenner, Matthias Dries, Lou van den van der Hoeven, Joris Logic Classical Analysis and ODEs Dynamical Systems We study relative differential closure in the context of Hardy fields. Using our earlier work on algebraic differential equations over Hardy fields, this leads to a proof of a conjecture of Boshernitzan (1981): the intersection of all maximal analytic Hardy fields agrees with that of all maximal Hardy fields. We also generalize a key ingredient in the proof, and describe a cautionary example delineating the boundaries of its applicability. |
| title | Relative differential closure in Hardy fields |
| topic | Logic Classical Analysis and ODEs Dynamical Systems |
| url | https://arxiv.org/abs/2412.10764 |