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A noted logician and philosopher addresses various forms of mathematical logic, discussing both theoretical underpinnings and practical applications. Author Hao Wang surveys the central concepts and theories...

During the last two decades, methods that originated within mathematical logic have exhibited powerful applications to Banach space theory, particularly set theory and model theory. This volume constitutes the...

While many books have been written about Bertrand Russell's philosophy and some on his logic, I. Grattan-Guinness has written the first comprehensive history of the mathematical background, content, and impact...

The primary purpose of this undergraduate text is to teach students to do mathematical proofs. It enables readers to recognize the elements that constitute an acceptable proof, and it develops their ability...

Combining stories of great philosophers, quotations, and riddles with the fundamentals of mathematical logic, this new textbook for first courses in mathematical logic was written by the subject's creative master....

Kenneth Arrow's pathbreaking impossibility theorem” was a watershed in the history of welfare economics, voting theory, and collective choice, demonstrating that there is no voting rule that satisfies the...

Hailed by the *Bulletin of the American Mathematical Society* as "easy to use and a pleasure to read," this research monograph is recommended for students and professionals interested in model theory and definability...

This landmark dissertation (1961) provides a systematic introduction to systems of modal logic and stands as the first presentation of what have become central ideas in philosophy of language and metaphysics,...

One of the twentieth century's most eminent mathematical writers offers insights into some of the more neglected aspects of arithmetic, algebra, and geometry. 1943 edition.

*Paradoxes of the Infinite* presents one of the most insightful, yet strangely unacknowledged, mathematical treatises of the 19^{th} century: Dr Bernard Bolzano's *Paradoxien*. This volume contains an adept translation...

This "best of" collection of works by Raymond Smullyan features logic puzzles, musings on mathematical logic and paradoxes, chess problems, and thoughts on the philosophy of religion, plus personal tributes...

This book provides a fun, hands-on approach to learning how mathematics and computing relate to the world around us and help us to better understand it. How can reposting on Twitter kill a movie’s opening...

A serious introductory treatment geared toward non-logicians, this survey traces the development of mathematical logic from ancient to modern times and discusses the work of Planck, Einstein, Bohr, Pauli, Heisenberg,...

A clear, comprehensive, and rigorous treatment develops the subject from elementary concepts to the construction and analysis of relatively complex logical languages. It then considers the application of symbolic...

Classic graduate-level introduction to theory of computability. Discusses general theory of computability, computable functions, operations on computable functions, Turing machines self-applied, unsolvable decision...

This bestselling textbook for higher-level courses was extensively revised in 1990 to accommodate developments in model theoretic methods. Topics include models constructed from constants, ultraproducts, and...

Focusing on topos theory's integration of geometric and logical ideas into the foundations of mathematics and theoretical computer science, this volume explores internal category theory, topologies and sheaves,...

Written by the nineteenth-century French philosophical founder of positivism, this comprehensive map of mathematical science assigns to each part of the complex whole its true position and value.

Comprehensive graduate-level account of constructive theory of first-order predicate calculus covers formal methods: algorithms and epitheory, brief treatment of Markov's approach to algorithms, elementary facts...

Rigorous introduction is simple enough in presentation and context for wide range of students. Symbolizing sentences; logical inference; truth and validity; truth tables; terms, predicates, universal quantifiers;...