## 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.## References

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## Additional Information

**Piotr Kowalski**- Affiliation: Department of Mathematics, Wrocław University, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
- MR Author ID: 658570
**Anand Pillay**- Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
- MR Author ID: 139610
- Received by editor(s): January 5, 2004
- Published electronically: January 21, 2005
- Additional Notes: The first author was supported by a postdoc under NSF Focused Research Grant DMS 01-00979 and the Polish KBN grant 2 P03A 018 24

The second author was partially supported by NSF grants DMS 00-70179 and DMS 01-00979 - © Copyright 2005 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**358**(2006), 167-181 - MSC (2000): Primary 32C38, 03C60
- DOI: https://doi.org/10.1090/S0002-9947-05-03820-1
- MathSciNet review: 2171228