Submission date: 20 August 2014

Abstract:

We give uniform companions for theories of partial differential and large fields of characteristic 0 that are expanded by relations and constants which are independent from the derivations. This is done by generalising the techniques presented by M. Tressl in his paper where he introduced uniform companions and the notion of large fields. As applications we provide an alternative uniform companion for partial differential henselian valued fields as well giving model companions for theories of partial differential with several orderings and valuations. We also apply our results to provide model complete theories of partial differential valued fields enriched by a predicate for a subfield of the residue field.

Mathematics Subject Classification: 03C10, 12H05, 12H20, 12J20, 03C64

Keywords and phrases: Differential Fields, Valued Fields, Ordered Fields, Topological Fields, Large Fields, Model Completeness, Quantifier Elimination, Completeness, Model Companionship, Model Completions, NIP.

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