Given an ordered field $K$, we compute the natural valuation and = skeleton of=20 the ordered multiplicative group $(K^{>0},\cdot ,1,<)$ in terms of = those=20 of the ordered additive group $(K,+,0,<)$. We use this computation to = provide=20 necessary and sufficient conditions on the value group $v(K)$ and = residue field=20 $\ovl{K}$, for the $\Lio$-equivalence of the above mentioned groups. We = then=20 apply the results to exponential fields, and describe $v(K)$ in that = case.=20 Finally, if $K$ is countable or a power series field, we derive = necessary and=20 sufficient conditions on $v(K)$ and $\ovl{K}$ for $K$ to be exponential. = In the=20 countable case, we get a structure theorem for $v(K)$.}=20

Last update: February 6, 1999 =