The uniform companion for large differential fields of characteristic 0
Author:
Marcus Tressl
Journal:
Trans. Amer. Math. Soc. 357 (2005), 39333951
MSC (2000):
Primary 03C65, 12H05; Secondary 03C10, 13N99
Published electronically:
May 10, 2005
MathSciNet review:
2159694
Fulltext PDF Free Access
Abstract 
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Similar Articles 
Additional Information
Abstract: We show that there is a theory UC of differential fields (in several commuting derivatives) of characteristic , which serves as a model companion for every theory of large and differential fields extending a model complete theory of pure fields. As an application, we introduce differentially closed ordered fields, differentially closed padic fields and differentially closed pseudofinite fields.
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 Z. Chatzidakis, L. van den Dries, A. Macintyre, Definable sets over finite fields. J. reine angew. Math. 427 (1992), 107135. MR 1162433 (94c:03049)
 [DL]
 J. Denef, L. Lipshitz, Power Series Solutions of Algebraic Differential Equations. Math. Ann. 267 (1984), 213238. MR 0738249 (85j:12010)
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 L. van den Dries, K. Schmidt, Bounds in the theory of polynomial rings over fields. A nonstandard approach. Invent. Math. 76 (1984), no. 1, 7791. MR 0739626 (85i:12016)
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 D. Eisenbud, Commutative Algebra with a View Toward Algebraic Geometry. Springer Graduate Texts in Mathematics 150, 1995. MR 1322960 (97a:13001)
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 G. Gallo, B. Mishra, Efficient Algorithms and Bounds for the WuRitt Characteristic Sets. Effective methods in algebraic geometry (Castiglioncello, 1990), 119142, Progr. Math., 94, BirkhäuserBoston, Boston, MA, 1991. MR 1106418 (92e:14058)
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 T. McGrail, The model theory of differential fields with finitely many commuting derivations. J. Symbolic Logic 65 (2000), no. 2, 885913. MR 1771092 (2001h:03066)
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 D. Pierce, Differential Forms in the Model Theory of Differential Fields. J. Symbolic Logic 68 (2003), no. 3, 923945. MR 2000487 (2004h:03080)
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Additional Information
Marcus Tressl
Affiliation:
NWFI Mathematik, 93040 Universität Regensburg, Germany
Email:
marcus.tressl@mathematik.uniregensburg.de
DOI:
http://dx.doi.org/10.1090/S0002994705039814
PII:
S 00029947(05)039814
Keywords:
Differential algebra,
differentially closed,
large field,
model theory,
model complete
Received by editor(s):
April 22, 2003
Published electronically:
May 10, 2005
Article copyright:
© Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
