The uniform companion for large differential fields of characteristic

Marcus Tressl

doi:10.1090/S0002-9947-05-03981-4

The uniform companion for large differential fields of characteristic

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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 pseudofinite fields.

Original language	English
Pages (from-to)	3933-3951
Number of pages	19
Journal	Transactions of the American Mathematical Society
Volume	357
Issue number	10
DOIs	https://doi.org/10.1090/S0002-9947-05-03981-4
Publication status	Published - 10 May 2005

Keywords

Differential algebra
Differentially closed
Large field
Model complete
Model theory

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10.1090/S0002-9947-05-03981-4

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AB - 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 pseudofinite fields.

KW - Differential algebra

KW - Differentially closed

KW - Large field

KW - Model complete

KW - Model theory

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DO - 10.1090/S0002-9947-05-03981-4

M3 - Article

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JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

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The uniform companion for large differential fields of characteristic

Abstract

Keywords

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