Submission date: 8 May 2023

Abstract:

We develop a first-order theory of ordered transexponential fields in the language {+,ċ,0,1,<,e,T}, where e and T stand for unary function symbols. While the archimedean models of this theory are readily described, the study of the non-archimedean models leads to a systematic examination of the induced structure on the residue field and the value group under the natural valuation. We establish necessary and sufficient conditions on the value group of an ordered exponential field (K,e) to admit a transexponential function T compatible with e. Moreover, we give a full characterisation of all countable ordered transexponential fields in terms of their valuation theoretic

Mathematics Subject Classification: 12J25, 03C64 (primary), 12J15, 26A12, 06F20, 12L12 (secondary)

Keywords and phrases:

Full text arXiv 2305.04607: pdf, ps.