 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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| |  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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 What Is Mathematical Logic?
by J. N. Crossley, C.J. Ash, C.J. Brickhill, J.C. Stillwell
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, Dirac, and others. 1972 edition.
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| |  A Profile of Mathematical Logic
by Howard DeLong
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 by this work.
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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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| |  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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 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 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 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 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 Symbolic Logic and Its Applications
by Rudolf Carnap
Clear, comprehensive, and rigorous treatment develops the subject from elementary concepts to the construction and analysis of relatively complex logical languages. Hundreds of problems, examples, and exercises. 1958 edition.
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 Logic and Boolean Algebra
by Bradford Henry Arnold
This volume concentrates on the structure of Boolean algebras and rings as developed through simpler algebraic systems. The algebra of logic and set theory appears as applications or illustrations throughout. 1962 edition.
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| |  Logic in Elementary Mathematics
by Robert M. Exner, Myron F. Rosskopf
This accessible, applications-related introductory treatment explores some of the structure of modern symbolic logic useful in the exposition of elementary mathematics. Numerous examples and exercises. 1959 edition.
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| |  The Logic of Chance
by John Venn
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 applications. 1888 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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| |  Set Theory and Logic
by Robert R. Stoll
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 theory, several algebraic theories, and 1st-order theories.
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 Studies in Logic and Probability
by George Boole
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.
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| |  Set Theory and the Continuum Hypothesis
by Paul J. Cohen
This exploration of a notorious mathematical problem is the work of the man who discovered the solution. The award-winning author employs intuitive explanations and detailed proofs in this self-contained treatment. 1966 edition. Copyright renewed 1994.
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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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 Proof Theory: Second Edition
by Gaisi Takeuti
This comprehensive monograph presents a detailed overview of creative works by the author and other 20th-century logicians that includes applications of proof theory to logic as well as other areas of mathematics. 1975 edition.
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| |  Topoi: The Categorial Analysis of Logic
by Robert Goldblatt
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 oriented readers.
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 Models and Ultraproducts : An Introduction
by A. B. Slomson, J. L. Bell
This first-year graduate text assumes only an acquaintance with set theory to explore homogeneous universal models, saturated structure, extensions of classical first-order logic, and other topics. 1974 edition.
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| |  Toposes and Local Set Theories: An Introduction
by J. L. Bell
This introduction to topos theory examines local set theories, fundamental properties of toposes, sheaves, locale-valued sets, and natural and real numbers in local set theories. 1988 edition.
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