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Model theory of partial differential fields: From commuting to noncommuting derivations
Author(s):
Michael
F.
Singer
Journal:
Proc. Amer. Math. Soc.
135
(2007),
1929-1934.
MSC (2000):
Primary 03C10;
Secondary 35A05, 12H05
Posted:
January 12, 2007
MathSciNet review:
2286106
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Abstract:
McGrail (2000) has shown the existence of a model completion for the universal theory of fields on which a finite number of commuting derivations act and, independently, Yaffe (2001) has shown the existence of a model completion for the univeral theory of fields on which a fixed Lie algebra acts as derivations. We show how to derive the second result from the first.
References:
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- 1.
- Ellis R. Kolchin, Differential algebraic groups, Pure and Applied Mathematics, vol. 114, Academic Press Inc., Orlando, FL, 1985. MR 0776230 (87i:12016)
- 2.
- Serge Lang, Algebra, 3rd ed., Addison-Wesley, New York, 1993. MR 1878556 (2003e:00003)
- 3.
- Tracey McGrail, The model theory of differential fields with finitely many commuting derivations, J. Symbolic Logic 65 (2000), no. 2, 885-913.MR 1771092 (2001h:03066)
- 4.
- David Pierce, Differential forms in the model theory of differential fields, J. Symbolic Logic 68 (2003), no. 3, 923-945. MR 2000487 (2004h:03080)
- 5.
- Gerald E. Sacks, Saturated model theory, W. A. Benjamin, Inc., Reading, Mass., 1972, Mathematics Lecture Note Series. MR 0398817 (53:2668)
- 6.
- Veeravalli S. Varadarajan, Lie Groups, Lie Algebras, and their Representations, Graduate Texts in Mathematics, no. 102, Springer-Verlag, New York, 1984.MR 0746308 (85e:22001)
- 7.
- Yoav Yaffe, Model completion of Lie differential fields, Ann. Pure Appl. Logic 107 (2001), no. 1-3, 49-86. MR 1807840 (2003i:03040)
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Additional Information:
Michael
F.
Singer
Affiliation:
Department of Mathematics, North Carolina State University, Box 8205, Raleigh, North Carolina 27695-8205
Email:
singer@math.ncsu.edu
DOI:
10.1090/S0002-9939-07-08653-4
PII:
S 0002-9939(07)08653-4
Received by editor(s):
November 25, 2005
Received by editor(s) in revised form:
January 21, 2006
Posted:
January 12, 2007
Additional Notes:
The preparation of this article was partially supported by NSF Grant CCR-0096842.
Communicated by:
Julia Knight
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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