Topological fields with a generic derivation

We study a class of tame G-theories T of topological fields and their G & delta;-extension T & delta;* by a generic derivation & delta;. The topological fields under consideration include henselian valued fields of characteristic 0 and real closed fields. We show that the associated expansion by a generic derivation has G-open core (i.e., every G & delta;-definable open set is G-definable) and derive both a cell decomposition theorem and a transfer result of elimination of imaginaries. Other tame properties of T such as relative elimination of field sort quantifiers, NIP and distality also transfer to T & delta;*. As an application, we derive consequences for the corresponding theories of dense pairs. In particular, we show that the theory of pairs of real closed fields (resp. of p-adically closed fields and real closed valued fields) admits a distal expansion. This gives a partial answer to a question of P. Simon.& COPY; 2023 Elsevier B.V. All rights reserved.