 Axiomatic Set Theory
by Patrick Suppes
Geared toward upper-level undergraduates and graduate students, this treatment examines the basic paradoxes and history of set theory and advanced topics such as relations and functions, equipollence, more. 1960 edition.
|  |
| |  An Outline of Set Theory
by James M. Henle
An innovative introduction to set theory, this volume is for undergraduate courses in which students work in groups and present their solutions to the class. Complete solutions. 1986 edition.
| |
|
 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.
| |
| |  Great Ideas of Modern Mathematics
by Jagjit Singh
Internationally famous expositor discusses differential equations, matrices, groups, sets, transformations, mathematical logic, and other important areas in modern mathematics. He also describes their applications to physics, astronomy, and other fields. 1959 edition.
| |
|
 Theory of Sets
by E. Kamke
Introductory treatment emphasizes fundamentals, covering rudiments; arbitrary sets and their cardinal numbers; ordered sets and their ordered types; and well-ordered sets and their ordinal numbers. "Exceptionally well written." — School Science and Mathematics.
| |
| |  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.
| |
|
 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.
| |
| |  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.
| |
|
 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.
| |
| |  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.
| |
|
 Recursive Analysis
by R. L. Goodstein
This text by a master in the field covers recursive convergence, recursive and relative continuity, recursive and relative differentiability, the relative integral, elementary functions, and transfinite ordinals. 1961 edition.
| |
| |  Set Theory and the Continuum Problem
by Raymond M. Smullyan, Melvin Fitting
A lucid, elegant, and complete survey of set theory, this three-part treatment explores axiomatic set theory, the consistency of the continuum hypothesis, and forcing and independence results. 1996 edition.
| |
|
 Boolean Algebra and Its Applications
by J. Eldon Whitesitt
Introductory treatment begins with set theory and fundamentals of Boolean algebra, proceeding to concise accounts of applications to symbolic logic, switching circuits, relay circuits, binary arithmetic, and probability theory. 1961 edition.
| |
| |  Abstract and Concrete Categories: The Joy of Cats
by Jiri Adamek, Horst Herrlich, George E Strecker
This up-to-date introductory treatment employs category theory to explore the theory of structures. Its unique approach stresses concrete categories and presents a systematic view of factorization structures. Numerous examples. 1990 edition, updated 2004.
| |
|
 The Philosophy of Mathematics: An Introductory Essay
by Stephan Körner
A distinguished philosopher surveys the mathematical views and influence of Plato, Aristotle, Leibniz, and Kant. He also examines the relationship between mathematical theories, empirical data, and philosophical presuppositions. 1968 edition.
| |
| |  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.
| |
|
 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.
| |
| |  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.
| |
|
| |  Introduction to the Theory of Sets
by Joseph Breuer, Howard F. Fehr
This undergraduate text develops its subject through observations of the physical world, covering finite sets, cardinal numbers, infinite cardinals, and ordinals. Includes exercises with answers. 1958 edition.
| |
|
 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.
| |
| |  Theory of Sets
by E. Kamke, Frederick Bagemihl
Clear and simple, this introduction to set theory employs the discoveries of Cantor, Russell, Weierstrass, Zermelo, Bernstein, Dedekind, and other mathematicians. It analyzes concepts and principles, offering numerous examples. 1950 edition.
| |
|
 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.
| |
| | |
 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.
| |
| |  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.
| |
|
 Basic Set Theory
by Azriel Levy
The first part of this advanced-level text covers pure set theory, and the second deals with applications and advanced topics (point set topology, real spaces, Boolean algebras, infinite combinatorics and large cardinals). 1979 edition.
| |
| |  Elements of the Theory of Functions and Functional Analysis
by A. N. Kolmogorov, S. V. Fomin
Advanced-level text, now available in a single volume, discusses metric and normed spaces, continuous curves in metric spaces, measure theory, Lebesque intervals, Hilbert space, more. Exercises. 1957 edition.
| |
|
 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.
| |
| | |
 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.
| |
| | |
| |  Axiomatic Set Theory
by Paul Bernays
A historical introduction by A. A. Fraenkel to the original Zermelo-Fraenkel form of set-theoretic axiomatics, plus Paul Bernays' independent presentation of a formal system of axiomatic set theory.
| |
|
 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.
| |
| |  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.
| |
|
