Quantifier elimination for algebraic 𝐷-groups

Kowalski, Piotr; Pillay, Anand

doi:10.1090/S0002-9947-05-03820-1

Quantifier elimination for algebraic $D$-groups
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by Piotr Kowalski and Anand Pillay PDF

Trans. Amer. Math. Soc. 358 (2006), 167-181 Request permission

Abstract:

We prove that if $G$ is an algebraic $D$-group (in the sense of Buium over a differentially closed field $(K,\partial )$ of characteristic $0$, then the first order structure consisting of $G$ together with the algebraic $D$-subvarieties of $G, G\times G,\dots$, has quantifier-elimination. In other words, the projection on $G^{n}$ of a $D$-constructible subset of $G^{n+1}$ is $D$-constructible. Among the consequences is that any finite-dimensional differential algebraic group is interpretable in an algebraically closed field.

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