Model Theory (Encyclopedia of Mathematics and its Applications Book 42) 1st Edition by Wilfrid Hodges (PDF)

Description

This is an up-to-date and integrated introduction to model theory, designed to be used for graduate courses (for students who are familiar with first-order logic), and as a reference for more experienced logicians and mathematicians. Model theory is concerned with the notions of definition, interpretation and structure in a very general setting, and is applied to a wide variety of other areas such as set theory, geometry, algebra (in particular group theory), and computer science (e.g. logic programming and specification). Professor Hodges emphasises definability and methods of construction, and introduces the reader to advanced topics such as stability. He also provides the reader with much historical information and a full bibliography, enhancing the book’s use as a reference.

User’s Reviews

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

⭐This is an excellent text on the model theory of first-order languages. A condensed version has also been published as: “A Shorter Model Theory.”This book is a classic. Its influence should be comparable to Keisler & Chang’s famous book as *the* standard account of the relationship between the language of f.o. logic and mathematical structures. (N.B. Chang & Keisler’s last edition is still useful alongside this book since the contents are not identical!)The text is clear and fluent, as one has come to expect from this remarkable author. The book includes a detailed bibliography and suggestions for further reading. The binding and typesetting are beautifully done as well.The short-comings are: (1) the large number of typos including an “incorrect lemma” (but with corrections available on the author’s homepage), (2) the almost exclusive concentration on (untyped) first-order languages and (3) avoidance of certain speacialized topics.All in all, this is an excellent book.

⭐The style is light, even glib, but still demanding. The prerequisites are not stated, but I would say undergraduate logic, graduate algebra, and a good deal of general mathematical experience. Motivation and context are very good and examples are frequent and clearly illustrative. What makes it challenging is that many details are glossed-over without the reader being warned about what knowledge is being assumed. His proofs also make many off-hand references rather than include every detail. Another thing I think it could use is more illustration of procedures; all of the examples seem to be of cases rather than methods. Still, explanations of specific points are often much clearer than in Marker.

⭐Vast in scope, full of careful attention to detail; proofs are generally clear and well-turned. Style is generally more accessible than that of a typical graduate textbook. Contains generous bibliography. This properly a reference and not a textbook, but would serve well the interested novice.

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