Set Theory And Its Logic

Author : Willard Van Orman Quine
Publisher : Harvard University Press
ISBN 13 : 9780674802070
Total Pages : 384 pages
Book Rating : 4.71/5 ( download)

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Download or read book Set Theory and Its Logic written by Willard Van Orman Quine and published by Harvard University Press. This book was released on 1969 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an extensively revised edition of W. V. Quine’s introduction to abstract set theory and to various axiomatic systematizations of the subject. The treatment of ordinal numbers has been strengthened and much simplified, especially in the theory of transfinite recursions, by adding an axiom and reworking the proofs. Infinite cardinals are treated anew in clearer and fuller terms than before. Improvements have been made all through the book; in various instances a proof has been shortened, a theorem strengthened, a space-saving lemma inserted, an obscurity clarified, an error corrected, a historical omission supplied, or a new event noted.

Author : Robert R. Stoll
Publisher : Courier Corporation
ISBN 13 : 0486139646
Total Pages : 512 pages
Book Rating : 4.47/5 ( download)

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Download or read book Set Theory and Logic written by Robert R. Stoll and published by Courier Corporation. This book was released on 2012-05-23 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Moshe Machover
Publisher : Cambridge University Press
ISBN 13 : 9780521479981
Total Pages : 304 pages
Book Rating : 4.83/5 ( download)

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Download or read book Set Theory, Logic and Their Limitations written by Moshe Machover and published by Cambridge University Press. This book was released on 1996-05-23 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introduction to set theory and logic that starts completely from scratch. The text is accompanied by many methodological remarks and explanations. A rigorous axiomatic presentation of Zermelo-Fraenkel set theory is given, demonstrating how the basic concepts of mathematics have apparently been reduced to set theory. This is followed by a presentation of propositional and first-order logic. Concepts and results of recursion theory are explained in intuitive terms, and the author proves and explains the limitative results of Skolem, Tarski, Church and Gödel (the celebrated incompleteness theorems). For students of mathematics or philosophy this book provides an excellent introduction to logic and set theory.

Author : Willard Van O QUINE
Publisher : Harvard University Press
ISBN 13 : 0674042425
Total Pages : 381 pages
Book Rating : 4.21/5 ( download)

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Download or read book Set Theory and Its Logic, Revised Edition written by Willard Van O QUINE and published by Harvard University Press. This book was released on 2009-06-30 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an extensively revised edition of Mr. Quine's introduction to abstract set theory and to various axiomatic systematizations of the subject. The treatment of ordinal numbers has been strengthened and much simplified, especially in the theory of transfinite recursions, by adding an axiom and reworking the proofs. Infinite cardinals are treated anew in clearer and fuller terms than before. Improvements have been made all through the book; in various instances a proof has been shortened, a theorem strengthened, a space-saving lemma inserted, an obscurity clarified, an error corrected, a historical omission supplied, or a new event noted.

Author : Norman T. Hamilton
Publisher : Courier Dover Publications
ISBN 13 : 0486830470
Total Pages : 288 pages
Book Rating : 4.76/5 ( download)

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Download or read book Set Theory: The Structure of Arithmetic written by Norman T. Hamilton and published by Courier Dover Publications. This book was released on 2018-05-16 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is formulated on the fundamental idea that much of mathematics, including the classical number systems, can best be based on set theory. 1961 edition.

Author : Michael Potter
Publisher : Clarendon Press
ISBN 13 : 0191556432
Total Pages : 362 pages
Book Rating : 4.32/5 ( download)

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Download or read book Set Theory and its Philosophy written by Michael Potter and published by Clarendon Press. This book was released on 2004-01-15 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Jacob T. Schwartz
Publisher : Springer Science & Business Media
ISBN 13 : 0857298089
Total Pages : 426 pages
Book Rating : 4.89/5 ( download)

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Download or read book Computational Logic and Set Theory written by Jacob T. Schwartz and published by Springer Science & Business Media. This book was released on 2011-07-16 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This must-read text presents the pioneering work of the late Professor Jacob (Jack) T. Schwartz on computational logic and set theory and its application to proof verification techniques, culminating in the ÆtnaNova system, a prototype computer program designed to verify the correctness of mathematical proofs presented in the language of set theory. Topics and features: describes in depth how a specific first-order theory can be exploited to model and carry out reasoning in branches of computer science and mathematics; presents an unique system for automated proof verification in large-scale software systems; integrates important proof-engineering issues, reflecting the goals of large-scale verifiers; includes an appendix showing formalized proofs of ordinals, of various properties of the transitive closure operation, of finite and transfinite induction principles, and of Zorn’s lemma.

Author : Iqbal H. Jebril
Publisher : CRC Press
ISBN 13 : 0429665989
Total Pages : 170 pages
Book Rating : 4.81/5 ( download)

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Download or read book Concise Introduction to Logic and Set Theory written by Iqbal H. Jebril and published by CRC Press. This book was released on 2021-09-30 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with two important branches of mathematics, namely, logic and set theory. Logic and set theory are closely related and play very crucial roles in the foundation of mathematics, and together produce several results in all of mathematics. The topics of logic and set theory are required in many areas of physical sciences, engineering, and technology. The book offers solved examples and exercises, and provides reasonable details to each topic discussed, for easy understanding. The book is designed for readers from various disciplines where mathematical logic and set theory play a crucial role. The book will be of interested to students and instructors in engineering, mathematics, computer science, and technology.

Author : Peter J. Cameron
Publisher : Springer Science & Business Media
ISBN 13 : 1447105893
Total Pages : 191 pages
Book Rating : 4.93/5 ( download)

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Download or read book Sets, Logic and Categories written by Peter J. Cameron and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: Set theory, logic and category theory lie at the foundations of mathematics, and have a dramatic effect on the mathematics that we do, through the Axiom of Choice, Gödel's Theorem, and the Skolem Paradox. But they are also rich mathematical theories in their own right, contributing techniques and results to working mathematicians such as the Compactness Theorem and module categories. The book is aimed at those who know some mathematics and want to know more about its building blocks. Set theory is first treated naively an axiomatic treatment is given after the basics of first-order logic have been introduced. The discussion is su pported by a wide range of exercises. The final chapter touches on philosophical issues. The book is supported by a World Wibe Web site containing a variety of supplementary material.

Author : J. Barkley Rosser
Publisher : Courier Dover Publications
ISBN 13 : 0486468984
Total Pages : 587 pages
Book Rating : 4.83/5 ( download)

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Download or read book Logic for Mathematicians written by J. Barkley Rosser and published by Courier Dover Publications. This book was released on 2008-12-18 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.