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We axiomatize a class of existentially closed exponential fields equipped with an $E$-derivation. We apply our results to the field of real numbers endowed with $exp(x)$ the classical exponential function defined by its power series expansion and to the field of p-adic numbers endowed with the function $exp(px)$ defined on the $p$-adic integers where $p$ is a prime number strictly bigger than $2$ (or with $exp(4x)$ when $p=2$).
For certain theories of existentially closed topological differential fields, we show that there is a strong relationship between $mathcal Lcup{D}$-definable sets and their $mathcal L$-reducts, where $mathcal L$ is a relational expansion of the field
In an extended abstract Ressayre considered real closed exponential fields and integer parts that respect the exponential function. He outlined a proof that every real closed exponential field has an exponential integer part. In the present paper, we
We answer two open questions about the model theory of valued differential fields introduced by Scanlon. We show that they eliminate imaginaries in the geometric language introduced by Haskell, Hrushovski and Macpherson and that they have the invaria
The following strong form of density of definable types is introduced for theories T admitting a fibered dimension function d: given a model M of T and a definable subset X of M^n, there is a definable type p in X, definable over a code for X and of
We continue the study of a class of topological $mathcal{L}$-fields endowed with a generic derivation $delta$, focussing on describing definable groups. We show that one can associate to an $mathcal{L}_{delta}$ definable group a type $mathcal{L}$-def