The uniform companion for large differential fields of characteristic 0

Marcus Tressl
2005 Transactions of the American Mathematical Society  
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.
doi:10.1090/s0002-9947-05-03981-4 fatcat:lykrzyswhbbc3kwj6hgqygnmcm