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Simplicity theory is an extension of stability theory to a wider class of structures, containing, among others, the random graph, pseudo-finite fields, and fields with a generic automorphism. Following Kim's proof of `forking symmetry' which implies a good behaviour of model-theoretic independence, this area of model theory has been a field of intense study. It has necessitated the development of some important new tools, most notably the model-theoretic treatment of hyperimaginaries (classes modulo type-definable equivalence relations). It thus provides a general notion of independence (and of rank in the supersimple case) applicable to a wide class of algebraic structures. The basic theory of forking independence is developed, and its properties in a simple structure are analyzed. No prior knowledge of stability theory is assumed; in fact many stability-theoretic results follow either from more general propositions, or are developed in side remarks. Audience: This book is intended both as an introduction to simplicity theory accessible to graduate students with some knowledge of model theory, and as a reference work for research in the field.

Model theory. --- Théorie des modèles --- Model theory --- Théorie des modèles --- Mathematical logic. --- Group theory. --- Commutative algebra. --- Commutative rings. --- Mathematical Logic and Foundations. --- Group Theory and Generalizations. --- Commutative Rings and Algebras. --- Rings (Algebra) --- Algebra --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism

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Model theory has, in recent years, made substantial contributions to semialgebraic, subanalytic, p-adic, rigid and diophantine geometry. This book provides the necessary background to understanding the theory and mathematics.

Model theory --- Geometry --- Algebraic fields. --- Algebraic fields --- Algebraic number fields --- Algebraic numbers --- Fields, Algebraic --- Algebra, Abstract --- Algebraic number theory --- Rings (Algebra) --- Mathematics --- Euclid's Elements --- Logic, Symbolic and mathematical

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Automatic theorem proving --- Logic programming --- 681.3*F3 --- 681.3*F41 --- 681.3*I23 --- Computer programming --- Automated theorem proving --- Theorem proving, Automated --- Theorem proving, Automatic --- Artificial intelligence --- Proof theory --- Logics and meanings of programs (Theory of computation) --- Mathematical logic: computability theory; computational logic; lambda calculus; logic programming; mechanical theorem proving; model theory; proof theory;recursive function theory--See also {681.3*F11}; {681.3*I22}; {681.3*I23} --- Deduction and theorem proving: answer/reason extraction; reasoning; resolution; metatheory; mathematical induction; logic programming (Artificial intelligence) --- Computer Science --- Mechanical Engineering - General --- Engineering & Applied Sciences --- Mechanical Engineering --- 681.3*I23 Deduction and theorem proving: answer/reason extraction; reasoning; resolution; metatheory; mathematical induction; logic programming (Artificial intelligence) --- 681.3*F41 Mathematical logic: computability theory; computational logic; lambda calculus; logic programming; mechanical theorem proving; model theory; proof theory;recursive function theory--See also {681.3*F11}; {681.3*I22}; {681.3*I23} --- 681.3*F3 Logics and meanings of programs (Theory of computation) --- Mathematics. --- Programming languages (Electronic computers). --- Computer logic. --- Mathematical logic. --- Artificial intelligence. --- Mathematical Logic and Foundations. --- Programming Languages, Compilers, Interpreters. --- Artificial Intelligence (incl. Robotics). --- Logics and Meanings of Programs. --- Mathematical Logic and Formal Languages. --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Computer science logic --- Logic, Symbolic and mathematical --- Computer languages --- Computer program languages --- Computer programming languages --- Machine language --- Languages, Artificial --- Math --- Science --- Logic, Symbolic and mathematical. --- Computer science. --- Logic design. --- Artificial Intelligence. --- Informatics --- Design, Logic --- Design of logic systems --- Digital electronics --- Electronic circuit design --- Logic circuits --- Switching theory --- Logic programming - Congresses --- Automatic theorem proving - Congresses

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Data mining --- Database searching --- 681.3*I2 <063> --- 681.3*H3 <063> --- 681.3*J2 <063> --- 681.3*H2 <063> --- 681.3*G3 <063> --- 681.3*I7 <063> --- 681.3*F42 <063> --- 681.3*F41 <063> --- 681.3*J2 <063> Physical sciences and engineering (Computer applications)--Congressen --- Physical sciences and engineering (Computer applications)--Congressen --- 681.3*I2 <063> Artificial intelligence. AI--Congressen --- Artificial intelligence. AI--Congressen --- Information storage and retrieval--Congressen --- Database management: security; integrity; protection--See also {?681.5*E5}--Congressen --- Probability and statistics: probabilistic algorithms (including Monte Carlo);random number generation; statistical computing; statistical software (Mathematics of computing)--Congressen --- Text processing (Computing methodologies)--See also {681.3*H4}--Congressen --- Grammars and other rewriting systems: decision problems; grammar types; parallel rewriting systems; parsing; thue systems (Mathematical logic and formal languages)--See also {681.3*D31}--Congressen --- Mathematical logic: computability theory; computational logic; lambda calculus; logic programming; mechanical theorem proving; model theory; proof theory;recursive function theory--See also {681.3*F11}; {681.3*I22}; {681.3*I23}--Congressen --- Computer science. --- Data structures (Computer science). --- Computer science --- Information storage and retrieval. --- Artificial intelligence. --- Computer Science. --- Artificial Intelligence (incl. Robotics). --- Data Structures, Cryptology and Information Theory. --- Popular Computer Science. --- Information Storage and Retrieval. --- Information Systems Applications (incl. Internet). --- Symbolic and Algebraic Manipulation. --- Mathematics. --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Computer mathematics --- Discrete mathematics --- Information structures (Computer science) --- Structures, Data (Computer science) --- Structures, Information (Computer science) --- File organization (Computer science) --- Abstract data types (Computer science) --- Informatics --- Science --- Mathematics --- Data structures (Computer scienc. --- Information storage and retrieva. --- Algebra --- Artificial Intelligence. --- Data Structures and Information Theory. --- Data processing. --- Information storage and retrieval systems. --- Automatic data storage --- Automatic information retrieval --- Automation in documentation --- Computer-based information systems --- Data processing systems --- Data storage and retrieval systems --- Discovery systems, Information --- Information discovery systems --- Information processing systems --- Information retrieval systems --- Machine data storage and retrieval --- Mechanized information storage and retrieval systems --- Computer systems --- Electronic information resources --- Data libraries --- Digital libraries --- Information organization --- Information retrieval --- Application software. --- Computer science—Mathematics. --- Application computer programs --- Application computer software --- Applications software --- Apps (Computer software) --- Computer software