On differentially closed ordered fields. (Ensembles définissables dans les corps ordonnés différentiellement clos.) (French. Abridged English version) Zbl 1237.03024
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.
Reviewer: Carlo Toffalori (Camerino)
MSC:
| 03C64 | Model theory of ordered structures; o-minimality |
| 03C60 | Model-theoretic algebra |
| 12L12 | Model theory of fields |
Keywords:
differentially closed ordered field; open core; o-minimal structure; elimination of imaginariesReferences:
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