Value groups and residue fields of models of real exponentiation

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 of cardinality κ and κ-saturated for an uncountable regular cardinal κ with κ Show more