 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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| |  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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| |  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: 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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| |  Undecidable Theories: Studies in Logic and the Foundation of Mathematics
by Alfred Tarski, Andrzej Mostowski, Raphael M. Robinson
This well-known book by the famed logician consists of three treatises: "A General Method in Proofs of Undecidability," "Undecidability and Essential Undecidability in Mathematics," and "Undecidability of the Elementary Theory of Groups." 1953 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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 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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| |  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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 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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 101 Puzzles in Thought and Logic
by C. R. Wylie, Jr.
Solve murder problems and robberies, see which fishermen are liars and how a blind man can identify color — purely by reasoning! Hours of mind-strengthening entertainment.
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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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 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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 Language, Truth and Logic
by Alfred Jules Ayer
Classic introduction to objectives and methods of schools of empiricism and linguistic analysis, especially of the logical positivism derived from the Vienna Circle. Topics: elimination of metaphysics, function of philosophy, more.
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| |  Mathematics and Logic
by Mark Kac, Stanislaw M. Ulam
Fascinating study of the origin and nature of mathematical thought, including relation of mathematics and science, 20th-century developments, impact of computers, more. Includes 34 illustrations. 1968 edition.
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 My Best Mathematical and Logic Puzzles
by Martin Gardner
The noted expert selects 70 of his favorite "short" puzzles, including such mind-bogglers as The Returning Explorer, The Mutilated Chessboard, Scrambled Box Tops, and dozens more involving logic and basic math. Solutions.
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| |  Puzzles in Math and Logic
by Aaron J. Friedland
100 original problems in math and logic, featuring permutations, combinations, properties of numbers, algebra, solid and plane geometry, logic, and probability. Even accomplished mathematicians are likely to find some surprises here. 31 drawings.
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 Symbolic Logic and the Game of Logic
by Lewis Carroll
Over 350 ingenious problems involving classical logic: logic expressed in symbols; syllogisms and the sorites diagrammed; logic as a game played with 2 diagrams and a set of counters.
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| |  Tractatus Logico-Philosophicus
by Ludwig Wittgenstein
In his proposal of the solution to most philosophic problems by means of a critical method of linguistic analysis, Wittgenstein sets the stage for the development of logical positivism. Introduction by Bertrand Russell.
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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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 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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 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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| |  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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