A Course in Model Theory: An Introduction to Contemporary Mathematical Logic (Universitext) by M. Klein
Springer; 2000 edition | June 1, 2000 | English | ISBN: 0387986553 | 443 pages | PDF | 38 MB
Translated from the French, this book is an introduction to first-order model theory. Starting from scratch, it quickly reaches the essentials, namely, the back-and-forth method and compactness, which are illustrated with examples taken from algebra. It also introduces logic via the study of the models of arithmetic, and it gives complete but accessible exposition of stability theory.