A course in model theory. An introduction to contemporary mathematical logic. Transl. from the French by Moses Klein
type: Item
instance of: scholarly article
title: A course in model theory. An introduction to contemporary mathematical logic. Transl. from the French by Moses Klein
zbMATH Open document ID: 0951.03002
author: Bruno Poizat
published in: Universitext
publication date: 2000-07-20T00:00:00Z
review text: It is with great satisfaction that I welcome the English translation of Poizat's \textit{Cours de théorie des modèles} (1985; Zbl 0583.03001) -- after all, this is the book where I learned not only my model and stability theory, but also my mathematical French. Incidentally, the French version is still available from the author, considerably cheaper than \textit{chez Springer}, and would be my first choice --- unless you think that mathematics is already difficult enough on its own. Except for Section 6.6 on real closed fields, some additional notes, a LATeX-assembled index with page numbers (much more convenient than the original), and the preface to the English edition, the content is unaltered from the French version (the Post Scriptum of the second edition has been incorporated into the main text, though, slightly changing the theorem numbering). Even the inimitable literary style of the author shines through, although at places the translation is inaccurate (e.g. \textit{la lumière \(\ldots\) eut été plus aveuglante} becomes \textit{the light \(\ldots\) was blinding}), or bows to a political correctness rather uncharacteristic for the author (the hitherto male reader suddenly and unaccountably becomes female on various occasions). Maybe the text is even a bit too unchanged: few mathematical books discuss the problems relating to \textit{dope} (usually called the DOP), and an extension of a type is not standardly referred to as its \textit{son}. However, on the whole I found the Gallicisms entertaining rather than distracting. As far as the mathematical content is concerned, the above mentioned review of the French version is still valid. The first half of the book is a very good, if slightly nonstandard, introduction to general model theory, with a heavy emphasis on semantic aspects and a healthy neglect of syntactics. The second half deals with stability theory, taking the Parisian approach to the subject via the fundamental order; as such it is a nice and hig…
Mathematics Subject Classification ID: 03-01
Mathematics Subject Classification ID: 03C45
Mathematics Subject Classification ID: 03-02
Mathematics Subject Classification ID: 03C07
zbMATH DE Number: 1479599
zbMATH Keywords: model theory
zbMATH Keywords: stability theory
zbMATH Keywords: local isomorphisms between structures
zbMATH Keywords: first-order language
zbMATH Keywords: elementary extensions
zbMATH Keywords: Löwenheim-Skolem-Tarski theorems
zbMATH Keywords: ultraproducts
zbMATH Keywords: compactness
zbMATH Keywords: saturated structures
zbMATH Keywords: algebraically and differentially closed fields
zbMATH Keywords: Boolean algebras
zbMATH Keywords: ultrametric spaces
zbMATH Keywords: existentially closed modules
zbMATH Keywords: prime models
zbMATH Keywords: fundamental order of types
zbMATH Keywords: saturated models
zbMATH Keywords: deviation
zbMATH Keywords: forking
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1479599