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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The uniform companion for large differential fields of characteristic 0


Author: Marcus Tressl
Journal: Trans. Amer. Math. Soc. 357 (2005), 3933-3951
MSC (2000): Primary 03C65, 12H05; Secondary 03C10, 13N99
Published electronically: May 10, 2005
MathSciNet review: 2159694
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Abstract: We show that there is a theory UC of differential fields (in several commuting derivatives) of characteristic $0$, 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 p-adic fields and differentially closed pseudo-finite fields.


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Additional Information

Marcus Tressl
Affiliation: NWF-I Mathematik, 93040 Universität Regensburg, Germany
Email: marcus.tressl@mathematik.uni-regensburg.de

DOI: http://dx.doi.org/10.1090/S0002-9947-05-03981-4
PII: S 0002-9947(05)03981-4
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.