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Automatic theorem proving --- Logic, Symbolic and mathematical --- Théorèmes --- Logique symbolique et mathématique --- Démonstration automatique --- Automatic theorem proving. --- Logic, Symbolic and mathematical. --- 681.3*I23 --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Automated theorem proving --- Theorem proving, Automated --- Theorem proving, Automatic --- Artificial intelligence --- Proof theory --- 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) --- Logic, symbolic and mathematical. --- Théorèmes --- Logique symbolique et mathématique --- Démonstration automatique

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This work presents the most important combinatorial ideas in partition calculus and discusses ordinary partition relations for cardinals without the assumption of the generalized continuum hypothesis. A separate section of the book describes the main partition symbols scattered in the literature. A chapter on the applications of the combinatorial methods in partition calculus includes a section on topology with Arhangel'skii's famous result that a first countable compact Hausdorff space has cardinality, at most continuum. Several sections on set mappings are included as well as an account of recent inequalities for cardinal powers that were obtained in the wake of Silver's breakthrough result saying that the continuum hypothesis can not first fail at a singular cardinal of uncountable cofinality. Provability, Computability and Reflection.

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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 collects, for the first time in one volume, contributions honoring Professor Raymond Smullyan’s work on self-reference. It serves not only as a tribute to one of the great thinkers in logic, but also as a celebration of self-reference in general, to be enjoyed by all lovers of this field. Raymond Smullyan, mathematician, philosopher, musician and inventor of logic puzzles, made a lasting impact on the study of mathematical logic; accordingly, this book spans the many personalities through which Professor Smullyan operated, offering extensions and re-evaluations of his academic work on self-reference, applying self-referential logic to art and nature, and lastly, offering new puzzles designed to communicate otherwise esoteric concepts in mathematical logic, in the manner for which Professor Smullyan was so well known. This book is suitable for students, scholars and logicians who are interested in learning more about Raymond Smullyan's work and life.

Logic, Symbolic and mathematical. --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Smullyan, Raymond M. --- Smullyan, Raymond --- Smallian, Reĭmond M. --- Смаллиан, Реймонд М. --- レイモンド・スマリヤン --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Logic. --- Information theory. --- Mathematical Logic and Foundations. --- Theory of Computation. --- Communication theory --- Communication --- Cybernetics --- Argumentation --- Deduction (Logic) --- Deductive logic --- Dialectic (Logic) --- Logic, Deductive --- Intellect --- Philosophy --- Psychology --- Science --- Reasoning --- Thought and thinking --- Methodology --- Mathematical logic. --- Computers. --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic brains --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Computer systems --- Machine theory --- Calculators --- Cyberspace --- Logic, symbolic and mathematical --- Logic - Philosophy --- Smullyan, Raymond, - 1919-2017 --- Logic