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Set theory is an autonomous and sophisticated field of mathematics that is extremely successful at analyzing mathematical propositions and gauging their consistency strength. It is as a field of mathematics that both proceeds with its own internal questions and is capable of contextualizing over a broad range, which makes set theory an intriguing and highly distinctive subject. This handbook covers the rich history of scientific turning points in set theory, providing fresh insights and points of view. Written by leading researchers in the field, both this volume and the Handbook as a whole

Logic --- Logique --- History. --- Histoire --- Induction (Logic) --- Philosophy --- History --- Logic. --- Argumentation --- Deduction (Logic) --- Deductive logic --- Dialectic (Logic) --- Logic, Deductive --- Intellect --- Psychology --- Science --- Reasoning --- Thought and thinking --- Methodology --- Set theory. --- Logic, Symbolic and mathematical. --- Many-valued logic. --- Nonmonotonic reasoning. --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Aggregates --- Classes (Mathematics) --- Ensembles (Mathematics) --- Mathematical sets --- Sets (Mathematics) --- Theory of sets --- Logic, Symbolic and mathematical --- Non-monotonic reasoning --- Logic, Many-valued --- Logic, Multivalued --- Logic, Variable-valued --- Multivalued logic --- Variable-valued logic --- Nonclassical mathematical logic --- Values

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This comprehensive book provides an adequate framework to establish various calculi of logical inference. Being an 'enriched' system of natural deduction, it helps to formulate logical calculi in an operational manner. By uncovering a certain harmony between a functional calculus on the labels and a logical calculus on the formulas, it allows mathematical foundations for systems of logic presentation designed to handle meta-level features at the object-level via a labeling mechanism, such as the D Gabbay's Labelled Deductive Systems. The book truly demonstrates that introducing 'labels' is us

Logic. --- Modality (Logic) --- Modal logic --- Logic --- Nonclassical mathematical logic --- Bisimulation --- Argumentation --- Deduction (Logic) --- Deductive logic --- Dialectic (Logic) --- Logic, Deductive --- Intellect --- Philosophy --- Psychology --- Science --- Reasoning --- Thought and thinking --- Methodology