Submission date: 6 October 2018

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.

Mathematics Subject Classification: Primary 03C64, Secondary 16W60

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Full text arXiv 1810.03029: pdf, ps.