 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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| |  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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 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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 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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| |  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 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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| |  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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 Natural Deduction: A Proof-Theoretical Study
by Dag Prawitz
The author of this study formulated the theories behind intuitionistic type theory and modern proof-theoretic semantics. He explains the principles of his proof-theoretical system, and he illustrates its applications to natural deduction. 1965 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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| |  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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| |  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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