Given a valuation v on field K, an extension v¯ to algebraic closure K¯ and w K(X). In this paper, we study common extensions w¯ of both the K¯(X). We describe set valuations using last key polynomial for its roots.

Abstract In this thesis, we study transfer principles in the context of certain Henselian valued fields, namely fields equicharacteristic $0$ , algebraically closed maximal Kaplansky and unramified mixed characteristic with perfect residue field. First, compute burden such a field terms its value group The is cardinal related to model theoretic complexity notion dimension associated $\text {NTP...

The purpose of this paper is to use generalized power series to provide two classes of examples of valued elds. In the rst set of examples the valued elds are henselian, in general not maximal, with given residue eld and value group. In the second set of examples, the valued elds are all maximal and their families of residue elds and value groups form chains. In both cases, these elds possess a...