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This two-volume work bridges the gap between introductory expositions of logic or set theory on one hand, and the research literature on the other. It can be used as a text in an advanced undergraduate or beginning graduate course in mathematics, computer science, or philosophy. The volumes are written in a user-friendly conversational lecture style that makes them equally effective for self-study or class use. Volume 1 includes formal proof techniques, a section on applications of compactness (including nonstandard analysis), a generous dose of computability and its relation to the incompleteness phenomenon, and the first presentation of a complete proof of Godel's 2nd incompleteness since Hilbert and Bernay's Grundlagen theorem.

Mathematische Logik --- MENGENLEHRE (MATHEMATIK) --- LEHRBÜCHER (DOKUMENTENTYP) --- MATHEMATICAL LOGIC --- logique mathématique --- THÉORIE DES ENSEMBLES (MATHÉMATIQUES) --- SET THEORY (MATHEMATICS) --- TEXTBOOKS (DOCUMENT TYPE) --- MANUELS POUR L'ENSEIGNEMENT (TYPE DE DOCUMENT) --- Mathematische Logik. --- MENGENLEHRE (MATHEMATIK). --- LEHRBÜCHER (DOKUMENTENTYP). --- MATHEMATICAL LOGIC. --- logique mathématique. --- THÉORIE DES ENSEMBLES (MATHÉMATIQUES). --- SET THEORY (MATHEMATICS). --- TEXTBOOKS (DOCUMENT TYPE). --- MANUELS POUR L'ENSEIGNEMENT (TYPE DE DOCUMENT). --- Logique mathématique. --- Logic, Symbolic and mathematical. --- Set theory. --- Aggregates --- Classes (Mathematics) --- Ensembles (Mathematics) --- Mathematical sets --- Sets (Mathematics) --- Theory of sets --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Logic, Symbolic and mathematical --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Logic, symbolic and mathematical

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Theory of knowledge --- Uncertainty (Information theory) --- Incertitude (Théorie de l'information) --- 003.54 --- Measure of uncertainty (Information theory) --- Shannon's measure of uncertainty --- System uncertainty --- Questions and answers --- Probability and statistics: probabilistic algorithms (including Monte Carlo);random number generation; statistical computing; statistical software (Mathematics of computing) --- Deduction and theorem proving: answer/reason extraction; reasoning; resolution; metatheory; mathematical induction; logic programming (Artificial intelligence) --- 681.3*I23 Deduction and theorem proving: answer/reason extraction; reasoning; resolution; metatheory; mathematical induction; logic programming (Artificial intelligence) --- 681.3*G3 Probability and statistics: probabilistic algorithms (including Monte Carlo);random number generation; statistical computing; statistical software (Mathematics of computing) --- Uncertainty (Information theory). --- Incertitude (Théorie de l'information) --- Logic, Symbolic and mathematical --- Reasoning --- 681.3*G3 --- 681.3*I23 --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Argumentation --- Ratiocination --- Reason --- Thought and thinking --- Judgment (Logic) --- Logic --- Information measurement --- Probabilities --- Artificial intelligence. Robotics. Simulation. Graphics --- Logic, symbolic and mathematical --- Logic, Symbolic and mathematical. --- Reasoning. --- Incertitude --- Raisonnement --- Logique mathématique --- Logique symbolique et mathématique --- Incertitude. --- Raisonnement. --- Logique mathématique. --- Artificial intelligence.