Exponential fields and Conway’s omega-map

Exponential fields and Conway’s omega-map

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 mode...

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Veröffentlicht in:Proceedings of the American Mathematical Society 2023-03, Vol.151 (6), p.2655-2669
Hauptverfasser: Berarducci, Alessandro, Kuhlmann, Salma, Mantova, Vincenzo, Matusinski, Mickaël
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container_title Proceedings of the American Mathematical Society
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creator Berarducci, Alessandro
Kuhlmann, Salma
Mantova, Vincenzo
Matusinski, Mickaël
description 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.
doi_str_mv 10.1090/proc/14577
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title Exponential fields and Conway’s omega-map
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