On the structure of nonarchimedean exponential fields I

Given an ordered fieldK, we compute the natural valuation and skeleton of the ordered multiplicative group (K>0, ·, 1, K,+,0,v(K) and residue field $$\bar K$$, for theL8e-equivalence of the above mentioned groups. We then apply the results to exponential fields, and describev(K) in that case. Finally, ifK is countable or a power series field, we derive necessary and sufficient conditions onv(K) and $$\bar K$$ forK to be exponential. In the countable case, we get a structure theorem forv(K).