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Introduction to Model Theory (Algebra, Logic and Applications Series Volume 15) Hardcover – October 31, 2000

ISBN-13: 978-9056992873 ISBN-10: 9056992872 Edition: 1st

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Product Details

  • Series: Algebra, Logic and Applications Series Volume 15 (Book 15)
  • Hardcover: 324 pages
  • Publisher: CRC Press; 1 edition (October 31, 2000)
  • Language: English
  • ISBN-10: 9056992872
  • ISBN-13: 978-9056992873
  • Product Dimensions: 0.8 x 6 x 9 inches
  • Shipping Weight: 1.4 pounds
  • Average Customer Review: 4.5 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon Best Sellers Rank: #14,184,156 in Books (See Top 100 in Books)

Editorial Reviews

Language Notes

Text: English (translation)
Original Language: German

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8 of 8 people found the following review helpful By B. Cody on December 5, 2007
Format: Paperback
I just finished a year long graduate course with the author and I highly recommend this book to anyone learning the basics of mathematical logic or model theory. The book is organized very well and contains LOTS of references to the original literature and historical points as well as LOTS of exercises throughout. We used the first half of the book in a first-year graduate introduction to logic and the second half in a second-year introduction to model theory. So, a knowledge of mathematical logic (though helpful) is not assumed.

The author only assumes a basic knowledge of advanced algebra (groups etc.). The book starts by introducing basic concepts such as signature, structures, satisfaction, truth etc. My favorite thing about the book is it's treatment of the compactness theorem. The compactness theorem is proven using ultraproducts. Something missing from most books (not this one) is a discussion of why the theorem is called the "compactness" theorem; the author discusses, stone space, which is the topological space asserted to be compact by the theorem. Other more advanced topics include the Lowenhiem-Skolem theorems, the omitting types theorem, and the structure theorem for strongly minimal theories.

The book would be suitable for a first course in model theory, or as an introduction to mathematical logic. I highly recommend this book.
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2 of 2 people found the following review helpful By C. F. Scherer on September 24, 2009
Format: Paperback Verified Purchase
I'm currently taking a graduate level "Foundations" class that is using this as our textbook. Most people in the class who haven't taken a general introduction to mathematical logic find this book somewhat confusing. Part I is just basically about getting the reader up to speed on notation and definitions that will be used in the other parts. If one wasn't familiar with these I think Part I could seem impossibly dense and labyrinthine. The sections we have read outside Part I are more leisurely and in my opinion are more carefully treated. There are also a few typos and awkwardly worded sentences. My advice would be to read (or be familiar with all the material in) "A Mathematical Introduction to Logic" by Enderton before buying this book.
One thing that does come through in the exposition is the sense of excitement and wonder that I think most people who study model theory feel and this adds a lot to the readability of the book. I also have to agree with a previous reviewer that the treatment of the compactness theorem is top notch!
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