Bøger af Alexander Prestel

This book presents, in a self-contained manner, the essential aspects of model theory needed to understand model theoretic algebra. Includes a complete proof of Ax and Kochen's work on Artin's conjecture about Diophantine properties of p-adic number fields.

Absolute values and their completions - such as the p-adic number fields - play an important role in number theory. In valuation theory, the notion of completion must be replaced by that of "Henselization". This book develops the theory of valuations as well as of Henselizations, based on the skills of a standard graduate course in algebra.

Positivity is one of the most basic mathematical concepts, involved in many areas of mathematics (analysis, real algebraic geometry, functional analysis, etc.). The main objective of the book is to give useful characterizations of polynomials. Beyond basic knowledge in algebra, only valuation theory as explained in the appendix is needed.