We present a framework for tame geometry on Henselian valued fields, which we call
Hensel minimality. In the spirit of o-minimality, which is key to real geometry and several …

We present a unifying theory of fields with certain classes of analytic functions, called fields
with analytic structure. Both real closed fields and Henselian valued fields are considered …

A MODEL COMPLETE THEORY OF VALUED £»-FIELDS The model theory of differential and
difference fields has been extensively studie Page 1 THE JOURNAL OF SYMBOLIC LOGTC …

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 …

The main results of this paper are a Cell Decomposition Theorem for Henselian valued
fields with analytic structure in an analytic Denef–Pas language, and its application to …

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 …

We give axiomatizations and prove quantifier elimination theorems for first-order theories of
unramified valued fields with an automorphism having a close interaction with the valuation …

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 …

The thesis addresses certain problems in the model theory of henselian fields, with a special
focus on decidability. Some new methods are introduced along the way, which are of …

We study interpretable sets in henselian and-henselian valued fields with value group
elementarily equivalent to Q or Z. Our first result is an Ax–Kochen–Ershov type principle for …