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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.
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Table of Contents

1. Naming of parts; 2. Classifying structures; 3. Structures that look alike; 4. Interpretations; 5. The first order case: compactness; 6. The countable case; 7. The existential case; 8. Saturation; 9. Structure and categoricity.

Reviews

'... up-to-date ... can serve as an introduction to applications of model theory in computer science.' L'Enseignement Mathematique ' ... a very readable introduction to the subject.' Mathematika 'This book contains rich material for a good introductory course in model theory ...' European Mathematical Society 'I have talked with students who first learned about model theory from this text, and overall it served them well. From his impressive work of 1993, Hodges has distilled an accessible introductory account. In doing so he has provided a valuable resource for a first study of model theory.' Carol Wood, International Journal of Symbolic Logic

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