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A geometric model of an arbitrary differentially closed field of characteristic zero. (English) Zbl 1465.12007

A differential field is a field equipped with commuting derivations. A differential field \(K\) is differentially closed if every finite system of differential equations with a solution in some differential field extending \(K\) already has a solution in \(K\). In the article models of ordinary differentially closed fields of characteristic zero are given. A universal extension of an ordinary differential field is constructed. A construction in terms of Nash functions of all algebraically closed fields of characteristic zero is given.

MSC:

12H05 Differential algebra
13N15 Derivations and commutative rings
14P20 Nash functions and manifolds
14P10 Semialgebraic sets and related spaces

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