Submission date: 8 March 2018

Abstract:

Let F be an archimedean field, G a divisible ordered abelian group and h a group exponential on G. A triple (F,G,h) is realised in a non-archimedean exponential field (K,exp) if the residue field of K under the natural valuation is F and the induced exponential group of (K,exp) is (G,h). We give a full characterisation of all triples (F,G,h) which can be realised in a model of real exponentiation in the following two cases: i) G is countable. ii) G is κ-saturated for an uncountable regular cardinal κ with κ<κ=κ.

Mathematics Subject Classification:

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Full text arXiv 1803.03153: pdf, ps.