Synopses & Reviews
Mathematical Logic and Model Theory: A Brief Introduction offers a streamlined yet easy-to-read introduction to mathematical logic and basic model theory. It presents, in a self-contained manner, the essential aspects of model theory needed to understand model theoretic algebra. As a profound application of model theory in algebra, the last part of this book develops a complete proof of Ax and Kochen's work on Artin's conjecture about Diophantine properties of p-adic number fields. The character of model theoretic constructions and results differs significantly from that commonly found in algebra, by the treatment of formulae as mathematical objects. It is therefore indispensable to first become familiar with the problems and methods of mathematical logic.
Synopsis
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.
Table of Contents
First-Order Logic.- Model Constructions.- Properties of Model Classes.- Model Theory of Several Algebraic Theories