Note sur les corps différentiellement clos valués

In the paper by Guzy and Point, Differential topological fields, the model-completion (OVF)D∗ of the theory of ordered valued differential fields OVFD is established. Models of this theory are closed ordered differential fields (the theory CODF was studied by Singer) which have a non-trivial convex (for the order) subring as valuation ring. Here we prove the valued analogue of a result of Singer: if K is a model of (OVF)D∗ then K(i) (i2=−1) is a model of the theory of differentially closed valued fields which is the model-completion of the theory of non-trivially valued differential fields of characteristic zero. To cite this article: N. Guzy, C. R. Acad. Sci. Paris, Ser. I 341 (2005).