On differentially closed ordered fields (Q640880)

Let \(M\) be an expansion of an ordered group endowed with a dense linear order. The open core of \(M\) is the structure having \(M\) as a domain and an \(n\)-ary relation for every non-empty definable subset of \(M^n\) (where \(n\) ranges over positive integers). The paper under review studies the open core of a differentially closed ordered field. It proves that such a field if definably complete and uniformly finite. By a result of Dolich, Miller and Steinhorn, it deduces that its open core is o-minimal. Moreover it shows that the theory of differentially closed ordered fields admits elimination of imaginaries.