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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...

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 "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...

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...

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...

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...

Popular account ranges from counting to mathematical logic and covers many concepts related to infinity: graphic representation of functions; pairings, other combinations; prime numbers; logarithms, circular...

With wit and clarity, the authors progress from simple arithmetic to calculus and non-Euclidean geometry. Their subjects: geometry, plane and fancy; puzzles that made mathematical history; tantalizing paradoxes;...

This classic undergraduate treatment examines the deductive method in its first part and explores applications of logic and methodology in constructing mathematical theories in its second part. Exercises appear...

Comprehensive and self-contained text examines the axiom's relative strengths and consequences, including its consistency and independence, relation to permutation models, and examples and counterexamples of...

A classic exposition of a branch of mathematical logic that uses category theory, this text is suitable for advanced undergraduates and graduate students and accessible to both philosophically and mathematically...

Authoritative compilation ranges from *The Mathematical Analysis of Logic* to the end of Boole's career. Includes *The Laws of Thought,* plus incomplete studies intended for a follow-up volume. 1952 edition.

Covers all areas, including operations on languages, context-sensitive languages, automata, decidability, syntax analysis, derivation languages, and more. Numerous worked examples, problem exercises, and elegant...

Examinations of arithmetic, geometry, and theory of integers; rational and natural numbers; complete induction; limit and point of accumulation; remarkable curves; complex and hypercomplex numbers; more. Includes...

No mathematical background is necessary to appreciate this classic of probability theory, which remains unsurpassed in its clarity and readability. It explores physical foundations, logical superstructure, and...

First English translation of revolutionary paper (1931) that established that even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. Introduction...

Explores sets and relations, the natural number sequence and its generalization, extension of natural numbers to real numbers, logic, informal axiomatic mathematics, Boolean algebras, informal axiomatic set...

This introduction to mathematical logic explores philosophical issues and Gödel's Theorem. Its widespread influence extends to the author of *Gödel, Escher, Bach*, whose Pulitzer Prize–winning book was inspired...

Part I of this coherent, well-organized text deals with formal principles of inference and definition. Part II explores elementary intuitive set theory, with separate chapters on sets, relations, and functions....

Third edition of popular undergraduate-level text offers historic overview, readable treatment of mathematics before Euclid, Euclid's Elements, non-Euclidean geometry, algebraic structure, formal axiomatics,...

smarTEST Prep: Guide to LSAT Logic Games presents a standardized and methodical approach to conquering the Logic Games section of the LSAT. This book helps readers to understand the fundamentals of logic games...

**How both logical and emotional reasoning can help us live better in our post-truth world**

In a world where fake news stories change election outcomes, has rationality become futile? In* The Art of Logic in an...*

What is math? How exactly does it work? And what do three siblings trying to share a cake have to do with it? In *How to Bake Pi*, math professor Eugenia Cheng provides an accessible introduction to the logic...

Burt C. Hopkins presents the first in-depth study of the work of Edmund Husserl and Jacob Klein on the philosophical foundations of the logic of modern symbolic mathematics. Accounts of the philosophical origins...

A masterful cultural history of mathematics from bestselling Italian mathematician and philosopher Paolo Zellini.

Is mathematics a discovery or an invention? Have we invented numbers or do they truly exist? What...

**How both logical and emotional reasoning can help us live better in our post-truth world**

In a world where fake news stories change election outcomes, has rationality become futile? In* The Art of Logic in an...*

**Puzzle lovers, rejoice!**

Bestselling math writer Alex Bellos has a challenge for you: 125 of the world’s best brainteasers from the last two millennia.

Armed with logic alone, you’ll detect counterfeit coins,...

**“A flawless compendium of flaws.” —Alice Roberts, PhD, anatomist, writer, and presenter of The Incredible Human Journey**

**The antidote to fuzzy thinking, with furry animals!**

Have you read (or stumbled into)...

Designed as a method for teaching correct mathematical thinking to high school students, this book contains a brilliantly constructed series of what the authors call "lapses," erroneous statements that are part...

Beginning with an introduction to the concepts of algebraic logic, this concise volume features ten articles by a prominent mathematician that originally appeared in journals from 1954 to 1959. Covering monadic...

**From atom bombs to rebounding slinkies, open your eyes to the mathematical magic in the everyday. **

Mathematics isn’t just for academics and scientists, a fact meteorologist and blogger Peter Lynch has spent...

Henry Ernest Dudeney (1857–1930) was an English author and mathematician who specialised in logic puzzles and mathematical games. He is known as one of the country's foremost creators of puzzles.

The Canterbury...

Over a period of 25 years as author of the Mathematical Games column for *Scientific American*, Martin Gardner devoted a column every six months or so to short math problems or puzzles. He was especially careful...

Mathematical induction — along with its equivalents, complete induction and well-ordering, and its immediate consequence, the pigeonhole principle — constitute essential proof techniques. Every mathematician...

This classic by one of the twentieth century's most prominent mathematicians offers a concise introduction to set theory. Suitable for advanced undergraduates and graduate students in mathematics, it employs...

Category theory has provided the foundations for many of the twentieth century's greatest advances in pure mathematics. This concise, original text for a one-semester course on the subject is derived from courses...

Yes, this is the Lewis Carroll who wrote Alice in Wonderland, and this work shows the same quirky humor. Here you see Carroll the mathematician at his playful best. Don't let the title of the first work mislead...

The book extends the development of probability logic_a logic using probability, not verity (true, false) as the basic semantic notion. The basic connectives 'not,' 'and,' and 'or' are described in depth to...