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Model theory

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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.

Model theory --- Logic, Symbolic and mathematical --- Model theory. --- Mathematical logic

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Model theory --- Modeles [Theorie des ] --- Modellentheorie --- Stabiliteit --- Stability --- Stabilité --- Mathematics

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The study of stable groups connects model theory, algebraic geometry and group theory. It analyses groups which possess a certain very general dependence relation (Shelah's notion of 'forking'), and tries to derive structural properties from this. These may be group-theoretic (nilpotency or solubility of a given group), algebro-geometric (identification of a group as an algebraic group), or model-theoretic (description of the definable sets). In this book, the general theory of stable groups is developed from the beginning (including a chapter on preliminaries in group theory and model theory), concentrating on the model- and group-theoretic aspects. It brings together the various extensions of the original finite rank theory under a unified perspective and provides a coherent exposition of the knowledge in the field.

Group theory. --- Model theory. --- Geometry, Algebraic. --- Algebraic geometry --- Geometry --- Logic, Symbolic and mathematical --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Model theory

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Model theory --- Théorie des modèles --- 510.6 --- #WWIS:ALTO --- Logic, Symbolic and mathematical --- Mathematical logic --- Model theory. --- 510.6 Mathematical logic --- Théorie des modèles --- Logique mathématique