Submission date: 14 June 2012.

Abstract:

This paper replaces Nr 438.

We consider a valued field of characteristic 0 with embedded residue field. We fix an additive complement to the valuation ring and its induced “constant term” map. We further assume that the valued field is endowed with an exponential map, and a derivation compatible with the exponential. We use a result of Ax to evaluate the transcendence degree of subfields generated by field elements which have constant term equal to 0 and are linearly independent. We apply our result to the examples of Logarithmic-Exponential power series fields, Exponential-Logarithmic power series fields, and Exponential Hardy fields.

Mathematics Subject Classification:

Keywords and phrases:

Full text arXiv 1204.0498: pdf, ps.