Set Theory and Its Logic
Set Theory and Its Logic

Author: Willard Van Orman Quine

Publisher: Harvard University Press

Published: 1969

Total Pages: 384

ISBN-13: 9780674802070

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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.

Set Theory and Logic
Set Theory and Logic

Author: Robert R. Stoll

Publisher: Courier Corporation

Published: 2012-05-23

Total Pages: 516

ISBN-13: 0486139646

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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.

Set Theory, Logic and Their Limitations
Set Theory, Logic and Their Limitations

Author: Moshe Machover

Publisher: Cambridge University Press

Published: 1996-05-23

Total Pages: 304

ISBN-13: 9780521479981

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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.

Concise Introduction to Logic and Set Theory
Concise Introduction to Logic and Set Theory

Author: Iqbal H. Jebril

Publisher: CRC Press

Published: 2021-09-30

Total Pages: 171

ISBN-13: 0429665989

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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.

Logic for Mathematicians
Logic for Mathematicians

Author: J. Barkley Rosser

Publisher: Courier Dover Publications

Published: 2008-12-18

Total Pages: 587

ISBN-13: 0486468984

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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.

Computational Logic and Set Theory
Computational Logic and Set Theory

Author: Jacob T. Schwartz

Publisher: Springer Science & Business Media

Published: 2011-07-16

Total Pages: 426

ISBN-13: 0857298089

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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.

Set Theory and Its Philosophy
Set Theory and Its Philosophy

Author: Michael D. Potter

Publisher: Clarendon Press

Published: 2004

Total Pages: 345

ISBN-13: 9780199269730

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A wonderful new book ... Potter has written the best philosophical introduction to set theory on the market - Timothy Bays, Notre Dame Philosophical Reviews.

Set Theory And Foundations Of Mathematics: An Introduction To Mathematical Logic - Volume I: Set Theory
Set Theory And Foundations Of Mathematics: An Introduction To Mathematical Logic - Volume I: Set Theory

Author: Douglas Cenzer

Publisher: World Scientific

Published: 2020-04-04

Total Pages: 222

ISBN-13: 9811201943

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This book provides an introduction to axiomatic set theory and descriptive set theory. It is written for the upper level undergraduate or beginning graduate students to help them prepare for advanced study in set theory and mathematical logic as well as other areas of mathematics, such as analysis, topology, and algebra.The book is designed as a flexible and accessible text for a one-semester introductory course in set theory, where the existing alternatives may be more demanding or specialized. Readers will learn the universally accepted basis of the field, with several popular topics added as an option. Pointers to more advanced study are scattered throughout the text.

Sets, Logic and Categories
Sets, Logic and Categories

Author: Peter J. Cameron

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 191

ISBN-13: 1447105893

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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.