The Axiom of Choice is the most controversial axiom in the entire history of mathematics. Yet it remains a crucial assumption not only in set theory but equally in modern algebra, analysis, mathematical logic, and topology (often under the name Zorn's Lemma). This treatment is the only full-length hi... read more
Customers who bought this book also bought:
Our Editors also recommend:
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.
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.
Evolution of Mathematical Concepts: An Elementary Study by Raymond L. Wilder Rather than a survey of the history or philosophy of modern mathematics, this treatment envisions mathematics as a broad cultural phenomenon, examining historic and social influences on such concepts as number and length. 1973 edition.
Introduction to the Foundations of Mathematics: Second Edition by Raymond L. Wilder Classic undergraduate text acquaints students with fundamental concepts and methods of mathematics. Topics include axiomatic method, set theory, infinite sets, groups, intuitionism, formal systems, mathematical logic, and much more. 1965 second edition.
Mathematics and the Imagination by Edward Kasner, James Newman With wit and clarity, the authors progress from simple arithmetic to calculus and non-Euclidean geometry. Their subjects: geometry, plane and fancy; puzzles that made mathematical history; tantalizing paradoxes; more. Includes 169 figures.
The World of Mathematics, Vol. 1 by James R. Newman Vol. 1 of a monumental 4-volume set includes a general survey of mathematics; historical and biographical information on prominent mathematicians throughout history; material on arithmetic, numbers and the art of counting, more.
The World of Mathematics, Vol. 2 by James R. Newman Vol. 2 of a monumental 4-volume set covers mathematics and the physical world, mathematics and social science, and the laws of chance, with non-technical essays by eminent mathematicians, economists, scientists, and others.
The World of Mathematics, Vol. 3 by James R. Newman Vol. 3 of a monumental 4-volume set covers such topics as statistics and the design of experiments, group theory, the mathematics of infinity, the unreasonableness of mathematics, the vocabulary of mathematics, and more.
The World of Mathematics, Vol. 4 by James R. Newman Vol. 4 of a monumental 4-volume set covers such topics as mathematical machines, mathematics in warfare, a mathematical theory of art, mathematics of the good, mathematics in literature, mathematics and music, and amusements.
History of Mathematics, Vol. I by David E. Smith Volume 1 of a two-volume history — from Egyptian papyri and medieval maps to modern graphs and diagrams. Non-technical chronological survey with thousands of biographical notes, critical evaluations, contemporary opinions on over 1,100 mathematicians.
History of Mathematics, Vol. II by David E. Smith Volume II of a two-volume history — from Egyptian papyri and medieval maps to modern graphs and diagrams. Evolution of arithmetic, geometry, trigonometry, calculating devices, algebra, calculus, more. Problems, recreations, and applications.
A Source Book in Mathematics by David Eugene Smith The writings of Newton, Leibniz, Pascal, Riemann, Bernoulli, and others in a comprehensive selection of 125 treatises dating from the Renaissance to the late 19th century — most unavailable elsewhere.
A Concise History of Mathematics: Fourth Revised Edition by Dirk J. Struik Compact, well-written survey ranges from the ancient Near East to 20th-century computer theory, covering Archimedes, Pascal, Gauss, Hilbert, and many others. "A work which is unquestionably one of the best." — Nature.
Makers of Mathematics by Stuart Hollingdale Each chapter of this accessible portrait of the evolution of mathematics examines the work of an individual — Archimedes, Descartes, Newton, Einstein, others — to explore the mathematics of his era. 1989 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.
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.
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.
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.
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.
An Introduction to Mathematical Logic by Richard E. Hodel Comprehensive overview, suitable for advanced undergraduates and graduate students, covers propositional logic; first-order languages and logic; incompleteness, undecidability, and indefinability; recursive functions; computability; and Hilbert's Tenth Problem. 1995 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.
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.
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.
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.
The Axiom of Choice is the most controversial axiom in the entire history of mathematics. Yet it remains a crucial assumption not only in set theory but equally in modern algebra, analysis, mathematical logic, and topology (often under the name Zorn's Lemma). This treatment is the only full-length history of the axiom in English, and is much more complete than the two other books on the subject, one in French and the other in Russian. This book covers the Axiom's prehistory of implicit uses in the 19th century, its explicit formulation by Zermelo in 1904, the firestorm of controversy that it caused — in England, France, Germany, Italy, and the U.S. — its role in stimulating his axiomatization of set theory in 1908, and its proliferating uses all over mathematics throughout the 20th century. The book is written so as to be accessible to the advanced mathematics undergraduate, but equally to be informative and stimulating to the professional mathematician. Most technical terms are defined in footnotes, making it accessible by students of the philosophy of mathematics as well. This new edition has an expanded bibliography and a new preface examining developments since its original 1982 publication.
Reprint of the Springer-Verlag, Inc., New York, 1982 edition.
This book was printed in the United States of America.
Dover books are made to last a lifetime. Our US book-manufacturing partners produce the highest quality books in the world and they create jobs for our fellow citizens. Manufacturing in the United States also ensures that our books are printed in an environmentally friendly fashion, on paper sourced from responsibly managed forests.