Value groups and residue fields of models of real exponentiation

@article{Krapp2019ValueGA,
title={Value groups and residue fields of models of real exponentiation},
author={L. S. Krapp},
journal={J. Log. Anal.},
year={2019},
volume={11}
}

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 $\kappa… CONTINUE READING