Quantifier elimination for algebraic D-groups

  title={Quantifier elimination for algebraic D-groups},
  author={Piotr Kowalski},
We prove that if G is an algebraic D-group (in the sense of Buium [B]) over a differentially closed field (K, ∂) of characteristic 0, then the first order structure consisting of G together with the algebraic D-subvarieties of G,G × G, . . ., has quantifier-elimination. In other words, the projection on Gn of a D-constructible subset of Gn+1 is Dconstructible. Among the consequences is that any finite-dimensional differential algebraic group is interpretable in an algebraically closed field. 

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