Exponential fields and Conway's omega-map
Logic
2024-01-24 v2
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.
Keywords
Cite
@article{arxiv.1810.03029,
title = {Exponential fields and Conway's omega-map},
author = {Alessandro Berarducci and Salma Kuhlmann and Vincenzo Mantova and Mickaël Matusinski},
journal= {arXiv preprint arXiv:1810.03029},
year = {2024}
}
Comments
15 pages; minor corrections and missing references; to appear in Proc. Amer. Math. Soc