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Exponential fields and Conway's omega-map

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arxiv 1810.03029 v2 pith:JHVFDGZ6 submitted 2018-10-06 math.LO

Alessandro Berarducci , Salma Kuhlmann , Vincenzo Mantova , Mickaël Matusinski This is my paper · ORCID
classification math.LO
keywords fieldsexponentialrealconwayfieldadditiveadmitsbounded
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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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  1. On Conway's Numbers and Games, the Von Neumann Universe, and Pure Set Theory

    math.LO 2025-01 conditional novelty 3.0 of 10

    Surreal numbers can be presented as sets of ordinals with a maximal 'birthday' element, giving a set-theoretic foundation equivalent to Gonshor's sign expansions and Conway's games.

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