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Exponential fields and Conway’s omega-map

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2023

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Berarducci, Alessandro
Mantova, Vincenzo

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Proceedings of the American Mathematical Society. American Mathematical Society (AMS). 2023, 151(9), pp. 2655-2669. ISSN 0002-9939. eISSN 1088-6826. Available under: doi: 10.1090/proc/14577

Zusammenfassung

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.

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510 Mathematik

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ISO 690BERARDUCCI, Alessandro, Salma KUHLMANN, Vincenzo MANTOVA, Mickael MATUSINSKI, 2023. Exponential fields and Conway’s omega-map. In: Proceedings of the American Mathematical Society. American Mathematical Society (AMS). 2023, 151(9), pp. 2655-2669. ISSN 0002-9939. eISSN 1088-6826. Available under: doi: 10.1090/proc/14577
BibTex
@article{Berarducci2023-03-21Expon-66611,
  year={2023},
  doi={10.1090/proc/14577},
  title={Exponential fields and Conway’s omega-map},
  number={9},
  volume={151},
  issn={0002-9939},
  journal={Proceedings of the American Mathematical Society},
  pages={2655--2669},
  author={Berarducci, Alessandro and Kuhlmann, Salma and Mantova, Vincenzo and Matusinski, Mickael}
}
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