Archive for Mathematical Logic 34 (3):145-182 (1995)

Given an ordered fieldK, we compute the natural valuation and skeleton of the ordered multiplicative group (K >0, ·, 1, <) in terms of those of the ordered additive group (K,+,0,<). We use this computation to provide necessary and sufficient conditions on the value groupv(K) and residue field $\bar K$ , for theL ∞ε-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)
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DOI 10.1007/BF01375519
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References found in this work BETA

Model Theory.Gebhard Fuhrken - 1976 - Journal of Symbolic Logic 41 (3):697-699.
On the Theory of Exponential Fields.Bernd I. Dahn & Helmut Wolter - 1983 - Mathematical Logic Quarterly 29 (9):465-480.

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