We develop here the algebra and model theory of the differential field of transseries, a
fascinating mathematical structure obtained by iterating a construction going back more than …

The subject originates in the 1950s with Abraham Robinson when he established the model
completeness of the theory of algebraically closed valued fields. In the 1960s Ax & Kochen …

Publisher Summary This chapter discusses the aspects of Symm, which relate directly to the
Witt vector constructions and their properties. The Witt vector construction is a very beautiful …

We show that the theory of the non-standard Frobenius automorphism, acting on an
algebraically closed valued field of equal characteristic 0, is NTP 2. More generally, in the …

We prove an analog of the Yomdin–Gromov lemma for, in analogy to results by Pila and
Wilkie, and by Bombieri and Pila, respectively. Along the way we prove, for definable …

We prove field quantifier elimination for valued fields endowed with both an analytic
structure that is endowed with its natural analytic structure and the lifting of the Frobenius. It …

Strictly convergent analytic structures Page 1 DOI 10.4171/JEMS/662 J. Eur. Math. Soc. 19,
107–149 c European Mathematical Society 2017 Raf Cluckers · Leonard Lipshitz Strictly …

We answer three related open questions about the model theory of valued differential fields
introduced by Scanlon. We show that they eliminate imaginaries in the geometric language …

Nous donnons un aperçu des développements de la théorie des modèles des nombres p-
adiques depuis les travaux de Denef sur la rationalité de séries de Poincaré, par une revue …

We study isomonodromicity of systems of parameterized linear differential equations and
related conjugacy properties of linear differential algebraic groups by means of differential …