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Axiomatic Set Theory

Mathematical logic --- Axiomatic set theory. --- Axiomatic set theory --- Axioms --- Logic, Symbolic and mathematical --- Set theory --- Logic, Symbolic and mathematical -- Periodicals. --- Logic, Symbolic and mathematical. --- Théorie des ensembles

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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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Provability, Computability and Reflection

Set theory. --- Descriptive set theory. --- Set theory --- Aggregates --- Classes (Mathematics) --- Ensembles (Mathematics) --- Mathematical sets --- Sets (Mathematics) --- Theory of sets --- Logic, Symbolic and mathematical --- Mathematics --- Descriptive set theory --- Théorie des ensembles. --- Théorie des ensembles --- Théorie descriptive des ensembles --- ELSEVIER-B EPUB-LIV-FT

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Les notions d'ordre, de classement, de rangement sont présentés dans de multiples activités et situations humaines. La formalisation mathématique de ces notions a permis d'abord le grand développement de la théorie des treillis, puis celui de structures ordonnées plus générales, notamment celles relevant des mathématiques discrètes. Les buts principaux de cet ouvrage qui comble un vide sont donc de: - donner les concepts et résultats fondamentaux sur les ensembles ordonnés finis, - présenter leurs usages dans des domaines variés (de la RO ou l’IA à la micro-économie), - signaler un certain nombre de résultats et de recherches en cours. Le lecteur sera ainsi à même de trouver tout ce qu'il a besoin de connaître sur ces structures sans devoir le rechercher dans de multiples revues relevant de disciplines variées.

Ordered sets. --- Computer science --- Knowledge representation (Information theory) --- Operations research. --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Mathematics. --- Representation of knowledge (Information theory) --- Artificial intelligence --- Information theory --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Sets, Ordered --- Set theory --- Mathematics --- Algebra. --- Order, Lattices, Ordered Algebraic Structures. --- Game Theory, Economics, Social and Behav. Sciences. --- Operations Research, Management Science. --- Math --- Science --- Mathematical analysis --- Ordered algebraic structures. --- Game theory. --- Management science. --- Games, Theory of --- Theory of games --- Mathematical models --- Quantitative business analysis --- Management --- Problem solving --- Operations research --- Statistical decision --- Algebraic structures, Ordered --- Structures, Ordered algebraic --- Algebra --- Ensembles ordonnés --- Théorie des ensembles

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In 1965 Lotfi Zadeh, a professor of electrical engineering at the University of California in Berkeley, published the first of his papers on his new Fuzzy Set Theory. Since the 1980s this mathematical theory of "unsharp amounts" has been applied in many different fields with great success. The word "fuzzy" has also become very well-known among non-scientists thanks to extensive advertising campaigns for fuzzy-controlled household appliances and to their prominent presence in the media, first in Japan and then in other countries. On the other hand, the story of how Fuzzy Set Theory and its earliest applications originated remains largely unknown. In this book, the history of Fuzzy Set Theory and the ways it was first used are incorporated into the history of 20th century science and technology. Influences from philosophy, system theory and cybernetics stemming from the earliest part of the 20th century are considered alongside those of communication and control theory from mid-century. Today, Fuzzy Set Theory is the core discipline of "soft computing," and provides new impetus for research in the field of Artificial Intelligence.

Fuzzy sets. --- Set theory. --- Ensembles flous --- Théorie des ensembles --- Fuzzy sets --- Set theory --- Algebra --- Applied Mathematics --- Civil Engineering --- Engineering & Applied Sciences --- Mathematics --- Civil & Environmental Engineering --- Physical Sciences & Mathematics --- Aggregates --- Classes (Mathematics) --- Ensembles (Mathematics) --- Mathematical sets --- Sets (Mathematics) --- Theory of sets --- Sets, Fuzzy --- Computer science. --- Artificial intelligence. --- Computer-aided engineering. --- Applied mathematics. --- Engineering mathematics. --- Computer Science. --- Computer-Aided Engineering (CAD, CAE) and Design. --- Appl.Mathematics/Computational Methods of Engineering. --- Artificial Intelligence (incl. Robotics). --- Logic, Symbolic and mathematical --- Fuzzy mathematics --- Computer aided design. --- Mathematical and Computational Engineering. --- Artificial Intelligence. --- 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 --- Engineering --- Engineering analysis --- Mathematical analysis --- CAD (Computer-aided design) --- Computer-assisted design --- Computer-aided engineering --- Design --- CAE --- Data processing