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Recommendations... Logic for Mathematicians
by J. Barkley Rosser
Examination of essential topics and theorems assumes no background in logic. "Undoubtedly a major addition to the literature of mathematical logic." — Bulletin of the American Mathematical Society. 1978 edition.
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| |  Satan, Cantor and Infinity: Mind-Boggling Puzzles
by Raymond M. Smullyan
A renowned mathematician tells stories of knights and knaves in an entertaining look at the logical precepts behind infinity, probability, time, and change. Requires a strong background in mathematics. Complete solutions.
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 The Elements of Mathematical Logic
by Paul C. Rosenbloom
This excellent introduction to mathematical logic provides a sound knowledge of the most important approaches, stressing the use of logical methods. "Reliable." — The Mathematical Gazette. 1950 edition.
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| |  Mathematical Logic: A First Course
by Joel W. Robbin
This self-contained text will appeal to readers from diverse fields and varying backgrounds. Topics include 1st-order recursive arithmetic, 1st- and 2nd-order logic, and the arithmetization of syntax. Numerous exercises; some solutions. 1969 edition.
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 The Axiom of Choice
by Thomas J. Jech
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 its use. 1973 edition.
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| |  Mathematical Logic
by Stephen Cole Kleene
Contents include an elementary but thorough overview of mathematical logic of 1st order; formal number theory; surveys of the work by Church, Turing, and others, including Gödel's completeness theorem, Gentzen's theorem, more.
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 Introduction to Logic
by Patrick Suppes
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. Ideal for undergraduates.
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| |  Basic Concepts of Mathematics and Logic
by Michael C. Gemignani
Intended as a first look at mathematics at the college level, this text emphasizes logic and set theory — counting, numbers, functions, ordering, probabilities, and other components of higher mathematics.
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Products in Logic | | |  | Alice in Puzzle-Land: A Carrollian Tale for Children Under Eighty
by Raymond M. Smullyan, Martin Gardner, Greer Fitting
Characters from Wonderland and Through the Looking-Glass populate these 88 puzzles involving word play, logic and metalogic, and philosophical paradoxes. The charmingly illustrated challenges range from easy to difficult and include solutions.
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| | The Axiom of Choice
by Thomas J. Jech
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 its use. 1973 edition.
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| | Basic Concepts of Mathematics and Logic
by Michael C. Gemignani
Intended as a first look at mathematics at the college level, this text emphasizes logic and set theory — counting, numbers, functions, ordering, probabilities, and other components of higher mathematics.
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|  | Boolean Reasoning: The Logic of Boolean Equations
by Frank Markham Brown
Concise text begins with overview of elementary mathematical concepts and outlines theory of Boolean algebras; defines operators for elimination, division, and expansion; covers syllogistic reasoning, solution of Boolean equations, functional deduction. 1990 edition.
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| |  | Computability and Unsolvability
by Prof. Martin Davis
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 problems, applications of general theory, mathematical logic, Kleene hierarchy, more.
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| |  | Elementary Induction on Abstract Structures
by Yiannis N. Moschovakis
Well-written research monograph, recommended for students and professionals interested in model theory and definability theory. "Easy to use and a pleasure to read." — Bulletin of the American Mathematical Society. 1974 edition.
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| | The Elements of Mathematical Logic
by Paul C. Rosenbloom
This excellent introduction to mathematical logic provides a sound knowledge of the most important approaches, stressing the use of logical methods. "Reliable." — The Mathematical Gazette. 1950 edition.
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|  | First Course in Mathematical Logic
by Patrick Suppes, Shirley Hill
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; universal specification and laws of identity; more.
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|  | First Order Mathematical Logic
by Angelo Margaris
Well-written undergraduate-level introduction begins with symbolic logic and set theory, followed by presentation of statement calculus and predicate calculus. Also covers first-order theories, completeness theorem, Godel's incompleteness theorem, much more. Exercises. Bibliography.
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|  | First-Order Logic
by Raymond M. Smullyan
This self-contained study is both an introduction to quantification theory and an exposition of new results and techniques in "analytic" or "cut free" methods. The focus is on the tableau point of view. Includes 144 illustrations.
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|  | Foundations and Fundamental Concepts of Mathematics
by Howard Eves
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, sets, more. Problems, some with solutions. Bibliography.
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|  | Foundations of Mathematical Logic
by Haskell B. Curry
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 about lattices, logical connectives, more. 1963 edition.
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|  | Introduction to Elementary Mathematical Logic
by A. A. Stolyar
Lucid, accessible exploration of propositional logic, propositional calculus, and predicate logic. Topics include computer science and systems analysis, linguistics, and problems in the foundations of mathematics. 1970 edition.
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|  | Introduction to Formal Languages
by György E. Révész
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 mathematical proofs. 1983 edition.
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| | Introduction to Logic
by Patrick Suppes
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. Ideal for undergraduates.
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|  | Introduction to Mathematical Philosophy
by Bertrand Russell
Seminal work focuses on concepts of number, order, relations, limits and continuity, propositional functions, descriptions and classes, more. Clear, accessible excursion into realm where mathematics and philosophy meet.
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| |  | Introduction to Proof in Abstract Mathematics
by Andrew Wohlgemuth
This undergraduate text teaches students what constitutes an acceptable proof, and it develops their ability to do proofs of routine problems as well as those requiring creative insights. 1990 edition.
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