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Rating: 
Summary: Hodges' Model Theory
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.
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Summary: Previous Review Suspect
Review: 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.
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Summary: Excellent
Review: 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.
Rating:
Summary: Excellent
Review: 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.
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Summary: Excellent
Review: Wilfrid Hodges is an excellent expositor. I have found the book a pleasure to read. This is how all textbooks should be...
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