A Shorter Model Theory [Paperback]

Wilfrid Hodges (Author)

Book Description

Publication Date: April 28, 1997 | ISBN-10: 0521587131 | ISBN-13: 978-0521587136

This is an up-to-date textbook of model theory taking the reader from first definitions to Morley's theorem and the elementary parts of stability theory. Besides standard results such as the compactness and omitting types theorems, it also describes various links with algebra, including the Skolem-Tarski method of quantifier elimination, model completeness, automorphism groups and omega-categoricity, ultraproducts, O-minimality and structures of finite Morley rank. The material on back-and-forth equivalences, interpretations and zero-one laws can serve as an introduction to applications of model theory in computer science. Each chapter finishes with a brief commentary on the literature and suggestions for further reading. This book will benefit graduate students with an interest in model theory.

Editorial Reviews

Review

"I have talked with students who first learned about model theory from this text, and overall it served them well. From his impressive work in 1993, Hodges has distilled an accessible introductory account. In doing so he has provided a valuable resource for a first study of model theory." International Joy of Symbolic Logic

Book Description

This is an up-to-date textbook of model theory taking the reader from first definitions to Morley's theorem and the elementary parts of stability theory. Besides standard results such as the compactness and omitting types theorems, it also describes various links with algebra, including the Skolem-Tarski method of quantifier elimination, model completeness, automorphism groups and omega-categoricity, ultraproducts, O-minimality and structures of finite Morley rank. The material on back-and-forth equivalences, interpretations and zero-one laws can serve as an introduction to applications of model theory in computer science. Each chapter finishes with a brief commentary on the literature and suggestions for further reading.

Product Details

• Paperback: 324 pages
• Publisher: Cambridge University Press (April 28, 1997)
• Language: English
• ISBN-10: 0521587131
• ISBN-13: 978-0521587136
• Product Dimensions: 8.9 x 6 x 1.2 inches
• Shipping Weight: 1.2 pounds (View shipping rates and policies)
• Average Customer Review: 4.7 out of 5 stars  See all reviews (6 customer reviews)
• Amazon Best Sellers Rank: #1,018,090 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

19 of 19 people found the following review helpful:

5.0 out of 5 stars Excellent, August 7, 2000

By 

"emredomanic" (.) - See all my reviews

This review is from: A Shorter Model Theory (Paperback)

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.

12 of 12 people found the following review helpful:

4.0 out of 5 stars Shorter not simpler, July 11, 2005

By 

Nathan Oakes (Ashland, Oregon) - See all my reviews

This review is from: A Shorter Model Theory (Paperback)

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.

8 of 8 people found the following review helpful:

4.0 out of 5 stars the butcher's daughter slices leaner cuts, April 1, 2007

By 

Michael De (St Andrews, Scotland) - See all my reviews
(REAL NAME)   

This review is from: A Shorter Model Theory (Paperback)

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.