Customer Reviews

A Shorter Model Theory

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This textbook is an efficient condensation of Hodges's bulkier and more leisurely "Model Theory". As such, it excludes some of the "fun" topics in the larger book as well as the nice bibliography. On the other hand, it is a truly excellent textbook for model theory and, in fact, for logic (for those with some idea of what *that* is.)

Personally, I would have liked to see the following topics at least mentioned: higher-order languages, typed languages, ultraproducts, game theory. Nevertheless, this book is still the best and clearest textbook for model theory.

This is a cut version of Hodges' _Model Theory_. The content that remains is mostly unaltered. The only significant new material is section 9.5 on Morley's theorem, which was previously in the exercises of section 12.2. Also, the end-of-chapter references and historical notes have been replaced by suggested readings, the phrasing has been tightened here and there, and the harder problems have been cut. From most of the chapters that were cut, key sections were saved and inserted elsewhere, making for a lot of rearranging. It's too bad the big text is so expensive, because a lot of interesting material was cut.

Hodges has a sharp, witty writing style. It's a model theory book that covers the standard results one would want such a text to cover (plus you can check the ToC yourself). It's a condensed version of his "Model Theory" which is generally compared to Chang and Keisler's of the same title. I haven't read either of these other ones so I can't compare them to "A Shorter Model Theory".

Be warned that many of the examples require at least some understanding of abstract algebra. So if you do just logic and have little to no background in algebra, you might want to pick some up before reading this. But it's not necessary.

The exercises seem well-chosen. There is no answer key. They occur at the end of each subsection of a chapter. There are on average four subsections per chapter, and the exercises require one to apply their knowledge of the subsection or a combination of subsections of the chapter. Sometimes they require going ahead a little, but usually they build on stuff from previous chapters. They vary in difficulty, so you can skip some of them if they prove too challenging. Each chapter also has "Suggested further readings".

The book is not as notation-heavy as some of the others I've quickly glanced at. I liked that. I found that some stuff could've used better or more thorough explanation, at least to someone who is self-studying, or studying in a small group, none of whose members has previously studied model theory at an intermediate level.

I highly recommend it. It's priced well, clear, and stylistically well-written and pleasing to read.

Wilfrid Hodges is an excellent expositor. I have found the book a pleasure to read. This is how all textbooks should be...

This is a highly regarded text on model theory, which is a branch of mathematical logic. What model theory is NOT is ". . . what is(sic) sounds like: mathematical models (of the physical and mathematical worlds)", which is a quote that appears in an earlier review.

This book and its 1993 expanded version are in the field of Mathematical Logic, and Hodges of London University shows that model theory in particular has had a remarkable variety of applications to other branches of mathematics, including computers (Prolog, undecidability, etc. - see my reviews of Penrose, Ablamowitz et al, etc.), geometry (see my reviews of advanced geometry via Clifford algebras, including Chisholm and geometric physics including Misner et al, and elementary geometry including Schaum's Outlines), topology (see my review of Greene's Elegant Universe which uses string theory and topology and also Carlip's book), algebra (see my Review of Weinberg's Gravitation and Cosmology which uses algebraic, topological, and analytic methods in general relativity, and Nachtmann's book which uses algebra in quantum theory), analysis/advanced calculus (see my review of Clarke, Yu, Nedyaev et al, Zwillinger's books, etc.), and so on. This book is in the Cambridge Encyclopedia of Mathematics and its Applications series, volume 42. Like most books of the Cambridge Encyclopedia series, it is very thorough up to the date of its publication - probably the most thorough book on model theory, which is roughly what is sounds like: mathematical models (of the physical and mathematical worlds). British Universities are among the world's greatest Creative Genius universities in math and physics, and this book is no exception. Most people should hire a reputable consultant or tutor to help them understand and "translate" the book, which will be well worth the effort in almost every field.