Quantifier elimination for algebraic groups
Authors:
Piotr Kowalski and Anand Pillay
Journal:
Trans. Amer. Math. Soc. 358 (2006), 167181
MSC (2000):
Primary 32C38, 03C60
Published electronically:
January 21, 2005
MathSciNet review:
2171228
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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 quantifierelimination. In other words, the projection on of a constructible subset of is constructible. Among the consequences is that any finitedimensional differential algebraic group is interpretable in an algebraically closed field.
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 [P2]
 A. Pillay, Modeltheoretic consequences of a theorem of Campana and Fujiki, Fundamenta Mathematicae, 174 (2002), 187192. MR 1927236 (2003g:03057)
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 A. Pillay, Two remarks on differential fields, preprint, http://www.math.uiuc.edu/ People/pillay/remarks.difffields.pdf
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 B. Zilber, Model theory and algebraic geometry, Proceedings of 10th Easter Conference in Berlin, 1993, Humboldt Univ. of Berlin.
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Additional Information
Piotr Kowalski
Affiliation:
Department of Mathematics, Wrocław University, pl. Grunwaldzki 2/4, 50384 Wrocław, Poland
Anand Pillay
Affiliation:
Department of Mathematics, University of Illinois at UrbanaChampaign, Urbana, Illinois 61801
DOI:
http://dx.doi.org/10.1090/S0002994705038201
PII:
S 00029947(05)038201
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 0100979 and the Polish KBN grant 2 P03A 018 24
The second author was partially supported by NSF grants DMS 0070179 and DMS 0100979
Article copyright:
© Copyright 2005 American Mathematical Society
