Quantifier elimination for algebraic -groups

Authors:
Piotr Kowalski and Anand Pillay

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

Published electronically:
January 21, 2005

MathSciNet review:
2171228

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove that if is an algebraic -group (in the sense of Buium over a differentially closed field of characteristic , then the first order structure consisting of together with the algebraic -subvarieties of , has quantifier-elimination. In other words, the projection on of a -constructible subset of is -constructible. Among the consequences is that any finite-dimensional differential algebraic group is interpretable in an algebraically closed field.

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Additional Information

**Piotr Kowalski**

Affiliation:
Department of Mathematics, Wrocław University, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

**Anand Pillay**

Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801

DOI:
https://doi.org/10.1090/S0002-9947-05-03820-1

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

Article copyright:
© Copyright 2005
American Mathematical Society