A Course in Model Theory: An Introduction to Contemporary Mathematical Logic (Universitext) by Bruno Poizat (PDF)

Description

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.

User’s Reviews

Editorial Reviews: Review “It is with great satisfaction that I welcome the English translation of Poizat’s Cours de théorie des modèles … .” (Frank Wagner, zbMATH 0951.03002, 2022)

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The book is a an excellent introduction to math logic/model theory. Unfortunately, the quality of printing is not very good. For example, one could only guess what is actually written at several places on pages 70 and 75.

⭐A great book for logic and model theory, it has different approaches to many topics like formulas and structures or Gödel’s theorems (it has the best proof that I’ve ever seen about them). It’s a very complete book, but its only weakness is that doesn’t have anything about Fraïssè limits.

⭐The first half of this book is a model-theoretic introduction to logic for beginning graduate students. It takes an unusual approach in that it emphasizes back-and-forth construction rather than formula satisfaction. The second half is a treatment of stability theory (ca. 1970s) meant for professionals. His style is entertaining, but he often gets to the point in a long and roundabout way. Important points are embedded in the text rather than isolated as definitions and lemmas. Just a couple of the early chapters have exercises and not very many. With the idiosyncratic style, dated approach, and nonstandard coverage, I wouldn’t try using this as a main text.

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