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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2018
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1810.03029 |
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| _version_ | 1866913203999473664 |
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| author | Berarducci, Alessandro Kuhlmann, Salma Mantova, Vincenzo Matusinski, Mickaël |
| author_facet | Berarducci, Alessandro Kuhlmann, Salma Mantova, Vincenzo Matusinski, Mickaël |
| contents | Inspired by Conway's surreal numbers, we study real closed fields whose value group is isomorphic to the additive reduct of the field. We call such fields omega-fields and we prove that any omega-field of bounded Hahn series with real coefficients admits an exponential function making it into a model of the theory of the real exponential field. We also consider relative versions with more general coefficient fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1810_03029 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Exponential fields and Conway's omega-map Berarducci, Alessandro Kuhlmann, Salma Mantova, Vincenzo Matusinski, Mickaël Logic Primary 03C64, Secondary 16W60 Inspired by Conway's surreal numbers, we study real closed fields whose value group is isomorphic to the additive reduct of the field. We call such fields omega-fields and we prove that any omega-field of bounded Hahn series with real coefficients admits an exponential function making it into a model of the theory of the real exponential field. We also consider relative versions with more general coefficient fields. |
| title | Exponential fields and Conway's omega-map |
| topic | Logic Primary 03C64, Secondary 16W60 |
| url | https://arxiv.org/abs/1810.03029 |