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Author | Robert R. Stoll | |

ISBN-10 | 9780486139647 | |

Release | 2012-05-23 | |

Pages | 512 | |

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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. |

Author | Patrick Suppes | |

ISBN-10 | 9780486136875 | |

Release | 2012-05-04 | |

Pages | 265 | |

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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. |

Author | Paul J. Cohen | |

ISBN-10 | 9780486469218 | |

Release | 2008-12-09 | |

Pages | 154 | |

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This exploration of a notorious mathematical problem is the work of the man who discovered the solution. Written by an award-winning professor at Stanford University, it employs intuitive explanations as well as detailed mathematical proofs in a self-contained treatment. This unique text and reference is suitable for students and professionals. 1966 edition. Copyright renewed 1994. |

Author | Patrick Suppes | |

ISBN-10 | 9780486138053 | |

Release | 2012-07-12 | |

Pages | 336 | |

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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. |

Author | James M. Henle | |

ISBN-10 | 9781461386803 | |

Release | 2012-12-06 | |

Pages | 146 | |

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This book is designed for use in a one semester problem-oriented course in undergraduate set theory. The combination of level and format is somewhat unusual and deserves an explanation. Normally, problem courses are offered to graduate students or selected undergraduates. I have found, however, that the experience is equally valuable to ordinary mathematics majors. I use a recent modification of R. L. Moore's famous method developed in recent years by D. W. Cohen [1]. Briefly, in this new approach, projects are assigned to groups of students each week. With all the necessary assistance from the instructor, the groups complete their projects, carefully write a short paper for their classmates, and then, in the single weekly class meeting, lecture on their results. While the em phasis is on the student, the instructor is available at every stage to assure success in the research, to explain and critique mathematical prose, and to coach the groups in clear mathematical presentation. The subject matter of set theory is peculiarly appropriate to this style of course. For much of the book the objects of study are familiar and while the theorems are significant and often deep, it is the methods and ideas that are most important. The necessity of rea soning about numbers and sets forces students to come to grips with the nature of proof, logic, and mathematics. In their research they experience the same dilemmas and uncertainties that faced the pio neers. |

Author | Joseph Breuer | |

ISBN-10 | 9780486154879 | |

Release | 2012-08-09 | |

Pages | 128 | |

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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. |

Author | Charles C Pinter | |

ISBN-10 | 9780486497082 | |

Release | 2014-07-23 | |

Pages | 256 | |

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"This accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. Each definition is accompanied by commentary that motivates and explains new concepts. A historical introduction is followed by discussions of classes and sets, functions, natural and cardinal numbers, the arithmetic of ordinal numbers, and related topics. 1971 edition with new material by the author"-- |

Author | Azriel Levy | |

ISBN-10 | 9780486150734 | |

Release | 2012-06-11 | |

Pages | 416 | |

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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. |

Author | Richard E. Hodel | |

ISBN-10 | 9780486497853 | |

Release | 2013 | |

Pages | 491 | |

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This comprehensive overview ofmathematical logic is designedprimarily for advanced undergraduatesand graduate studentsof mathematics. The treatmentalso contains much of interest toadvanced students in computerscience and philosophy. Topics include propositional logic;first-order languages and logic; incompleteness, undecidability,and indefinability; recursive functions; computability;and Hilbert’s Tenth Problem.Reprint of the PWS Publishing Company, Boston, 1995edition. |

Author | Raymond M. Smullyan | |

ISBN-10 | 0486474844 | |

Release | 2010 | |

Pages | 315 | |

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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. |

Author | Stephen Cole Kleene | |

ISBN-10 | 9780486317076 | |

Release | 2013-04-22 | |

Pages | 416 | |

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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. |

Author | E. Kamke | |

ISBN-10 | 9780486450834 | |

Release | 2006 | |

Pages | 144 | |

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This introduction to the theory of sets employs the discoveries of Cantor, Russell, Weierstrass, Zermelo, Bernstein, Dedekind, and others. It analyzes concepts and principles, offering numerous examples. Topics include the rudiments of set theory, arbitrary sets and their cardinal numbers, ordered sets and their order types, and well-ordered sets and their ordinal numbers. 1950 edition. |

Author | J. Barkley Rosser | |

ISBN-10 | 9780486468983 | |

Release | 2008-12-18 | |

Pages | 574 | |

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Hailed by the Bulletin of the American Mathematical Society as "undoubtedly a major addition to the literature of mathematical logic," this volume examines the essential topics and theorems of mathematical reasoning. No background in logic is assumed, and the examples are chosen from a variety of mathematical fields. Starting with an introduction to symbolic logic, the first eight chapters develop logic through the restricted predicate calculus. Topics include the statement calculus, the use of names, an axiomatic treatment of the statement calculus, descriptions, and equality. Succeeding chapters explore abstract set theory—with examinations of class membership as well as relations and functions—cardinal and ordinal arithmetic, and the axiom of choice. An invaluable reference book for all mathematicians, this text is suitable for advanced undergraduates and graduate students. Numerous exercises make it particularly appropriate for classroom use. |

Author | Stephen Pollard | |

ISBN-10 | 9780486805825 | |

Release | 2015-07-20 | |

Pages | 192 | |

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The primary mechanism for ideological and theoretical unification in modern mathematics, set theory forms an essential element of any comprehensive treatment of the philosophy of mathematics. This unique approach to set theory offers a technically informed discussion that covers a variety of philosophical issues. Rather than focusing on intuitionist and constructive alternatives to the Cantorian/Zermelian tradition, the author examines the two most important aspects of the current philosophy of mathematics, mathematical structuralism and mathematical applications of plural reference and plural quantification. Clearly written and frequently cited in the mathematical literature, this book is geared toward advanced undergraduates and graduate students of mathematics with some aptitude for mathematical reasoning and prior exposure to symbolic logic. Suitable as a source of supplementary readings in a course on set theory, it also functions as a primary text in a course on the philosophy of mathematics. |

Author | Michael Potter | |

ISBN-10 | 9780191556432 | |

Release | 2004-01-15 | |

Pages | 360 | |

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Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science. |

Author | Raymond M. Smullyan | |

ISBN-10 | 0486683702 | |

Release | 1995 | |

Pages | 158 | |

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Considered the best book in the field, this completely 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 in on the tableau point of view. Topics include trees, tableau method for propositional logic, Gentzen systems, more. Includes 144 illustrations. |

Author | Moshe Machover | |

ISBN-10 | 0521479983 | |

Release | 1996-05-23 | |

Pages | 288 | |

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Rigorous coverage of logic and set theory for students of mathematics and philosophy. |