Exponential fields and Conway's omega-map
Alessandro Berarducci, Salma Kuhlmann, Vincenzo Mantova, Mickaël Matusinski
Abstract
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.