Submission date: 24 July 2015.

Abstract:

Let T be an NIP L-theory and \widetilde{T} be an enrichment. We give a sufficient condition on \widetilde{T} such that for every type over a models of \widetilde{T} which is definable (respectively invariant), the underlying L-type is also definable (respectively invariant) as an L-type. Besides, we generalise to this relative setting work of Simon and Starchenko on the density of definable types among non forking types. These results are then applied to the Scanlon's model completion of valued differential fields.

Mathematics Subject Classification:

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Full text arXiv 1507.06863: pdf, ps. x