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Forcing (Model theory) --- Model theory

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Provability, Computability and Reflection

Mathematical logic --- Model theory. --- Axiomatic set theory. --- Forcing (Model theory). --- Logic, Symbolic and mathematical --- Logique mathématique --- Model theory --- Théorie des modèles --- Forcing (Model theory) --- Forcing (mathématiques) --- Intuitionistic mathematics. --- Mathématiques intuitionnistes. --- Axiomatic set theory --- Théorie des modèles --- Théorie axiomatique des ensembles --- Forcing (Théorie des modèles) --- EPUB-LIV-FT ELSEVIER-B --- Logic, Symbolic and mathematical -- Periodicals. --- Logic, Symbolic and mathematical. --- 510.2 --- Axioms --- Set theory --- 510.2 Foundations of mathematics --- Foundations of mathematics

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This book, translated from the French, is an introduction to first-order model theory. The first six chapters are very basic: starting from scratch, they quickly reach the essential, namely, the back-and-forth method and compactness, which are illustrated with examples taken from algebra. The next chapter introduces logic via the study of the models of arithmetic, and the following is a combinatorial tool-box preparing for the chapters on saturated and prime models. The last ten chapters form a rather complete but nevertheless accessible exposition of stability theory, which is the core of the subject.

Model theory --- Théorie des modèles --- Model theory. --- Théorie des modèles --- Logic, Symbolic and mathematical --- Mathematical logic. --- Mathematical Logic and Foundations. --- 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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This volume contains the proceedings of the ninth international workshop on logic-based program synthesis and transformation (LOPSTR’99) which was held in Venice (Italy), September 22-24, 1999. LOPSTRistheannualworkshopandforumforresearchersinthelogic-based program development stream of computational logic. The main focus used to be on synthesis and transformation of logic programs, but the workshop is open to contributions on logic-based program development in any paradigm. Previous workshops were held in Manchester, UK (1991, 1992), Louvain-la-Neuve, B- gium (1993), Pisa, Italy (1994), Arnhem, The Netherlands (1995), Stockholm, Sweden (1996), Leuven, Belgium (1997), and Manchester, UK (1998). LOPSTR is a real workshop in the sense that it is a friendly and lively forum for presenting recent and current research as well as discussing future trends. Formal proceedings of the workshop are produced only after the workshop and contain only those papers selected by the program committee after a second refereeing process. The program committee of LOPSTR’99 accepted 20 extended abstracts for presentation at the workshop; then selected 14 papers for inclusion in the po- workshop proceedings. Selected papers cover all the main streams of LOPSTR’s topics: synthesis, specialization, transformation, analysis, and veri?cation. Ve- ?cation, transformation, and specialization methods are applied to functional, constraint, logic, and imperative programming.

681.3*D16 --- Logic programming --- 681.3*D11 --- 681.3*F31 --- 681.3*F41 --- 681.3*I22 --- 681.3*D11 Applicative (functional) programming --- Applicative (functional) programming --- 681.3*I22 Automatic programming: automatic analysis of algorithms program modification program synthesis program transformation program verification (Artificialintelligence)--See also {681.3*D12} {681.3*F31} --- Automatic programming: automatic analysis of algorithms program modification program synthesis program transformation program verification (Artificialintelligence)--See also {681.3*D12} {681.3*F31} --- 681.3*F41 Mathematical logic: computability theory computational logic lambda calculus logic programming mechanical theorem proving model theory proof theoryrecursive function theory--See also {681.3*F11} {681.3*I22} {681.3*I23} --- Mathematical logic: computability theory computational logic lambda calculus logic programming mechanical theorem proving model theory proof theoryrecursive function theory--See also {681.3*F11} {681.3*I22} {681.3*I23} --- 681.3*F31 Specifying anf verifying and reasoning about programs: assertions invariants mechanical verification pre- and post-conditions (Logics and meanings of programs)--See also {681.3*D21} {681.3*D24} {681.3*D31} {681.3*E1} --- Specifying anf verifying and reasoning about programs: assertions invariants mechanical verification pre- and post-conditions (Logics and meanings of programs)--See also {681.3*D21} {681.3*D24} {681.3*D31} {681.3*E1} --- Computerwetenschap--?*D16 --- Computer science. --- Software engineering. --- Computer programming. --- Computer logic. --- Mathematical logic. --- Artificial intelligence. --- Computer Science. --- Software Engineering/Programming and Operating Systems. --- Logics and Meanings of Programs. --- Programming Techniques. --- Artificial Intelligence (incl. Robotics). --- Mathematical Logic and Formal Languages. --- 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 --- Computers --- Electronic computer programming --- Electronic data processing --- Electronic digital computers --- Programming (Electronic computers) --- Coding theory --- Computer software engineering --- Engineering --- Informatics --- Science --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Programming --- 681.3*I22 Automatic programming: automatic analysis of algorithms; program modification; program synthesis; program transformation; program verification (Artificialintelligence)--See also {681.3*D12}; {681.3*F31} --- Automatic programming: automatic analysis of algorithms; program modification; program synthesis; program transformation; program verification (Artificialintelligence)--See also {681.3*D12}; {681.3*F31} --- 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} --- 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*F31 Specifying anf verifying and reasoning about programs: assertions; invariants; mechanical verification; pre- and post-conditions (Logics and meanings of programs)--See also {681.3*D21}; {681.3*D24}; {681.3*D31}; {681.3*E1} --- Specifying anf verifying and reasoning about programs: assertions; invariants; mechanical verification; pre- and post-conditions (Logics and meanings of programs)--See also {681.3*D21}; {681.3*D24}; {681.3*D31}; {681.3*E1} --- Logic design. --- Artificial Intelligence. --- Design, Logic --- Design of logic systems --- Digital electronics --- Electronic circuit design --- Logic circuits --- Switching theory --- Logic programming - Congresses