Presenting recent developments and applications, the book focuses on four main topics in current model theory: 1) the model theory of valued fields; 2) undecidability in arithmetic; 3) NIP theories; and 4) the model theory of real and complex exponentiation. Young researchers in model theory will particularly benefit from the book, as will more senior researchers in other branches of mathematics.

Presentation of a seminar result (Wilkie's o-minimality of the real exponential field) through a series of exercises Extended expository article on the model theory of valued fields, an area with many current researchers and a lack of good expositions Wide-ranging and up-to-date overview of undecidability and Hilbert's Tenth Problem, linking model theory, number theory, and algebraic geometry Exposition of recent breakthrough in abstract model theory, around NIP theories

Inhalt

Some themes around first order theories without the independence property.- Lectures on the model theory of real and complex exponentiation.- Lectures on the model theory of valued fields.- Undecidability in number theory.