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.
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.
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.
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.
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.
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.
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.
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.
Download or read book Introduction to Mathematical Logic written by Jerome Malitz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended as an undergraduate senior level or beginning graduate level text for mathematical logic. There are virtually no prere quisites, although a familiarity with notions encountered in a beginning course in abstract algebra such as groups, rings, and fields will be useful in providing some motivation for the topics in Part III. An attempt has been made to develop the beginning of each part slowly and then to gradually quicken the pace and the complexity of the material. Each part ends with a brief introduction to selected topics of current interest. The text is divided into three parts: one dealing with set theory, another with computable function theory, and the last with model theory. Part III relies heavily on the notation, concepts and results discussed in Part I and to some extent on Part II. Parts I and II are independent of each other, and each provides enough material for a one semester course. The exercises cover a wide range of difficulty with an emphasis on more routine problems in the earlier sections of each part in order to familiarize the reader with the new notions and methods. The more difficult exercises are accompanied by hints. In some cases significant theorems are devel oped step by step with hints in the problems. Such theorems are not used later in the sequence.
Download or read book Elements of Mathematical Logic and Set Theory written by Jerzy Słupecki and published by Pergamon. This book was released on 1967 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Problems in Set Theory Mathematical Logic and the Theory of Algorithms written by Igor Lavrov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Problems in Set Theory, Mathematical Logic and the Theory of Algorithms by I. Lavrov & L. Maksimova is an English translation of the fourth edition of the most popular student problem book in mathematical logic in Russian. It covers major classical topics in proof theory and the semantics of propositional and predicate logic as well as set theory and computation theory. Each chapter begins with 1-2 pages of terminology and definitions that make the book self-contained. Solutions are provided. The book is likely to become an essential part of curricula in logic.
Download or read book Abstract Set Theory written by Abraham Adolf Fraenkel and published by . This book was released on 1968 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Geometry of Ren Descartes written by René Descartes and published by Open Court. This book was released on 1925 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: The great work that founded analytical geometry. Includes the original French text, Descartes' own diagrams, and the definitive Smith-Latham translation. "The greatest single step ever made in the progress of the exact sciences." -- John Stuart Mill.
Download or read book A First Course in Mathematical Logic and Set Theory written by Michael L. O'Leary and published by John Wiley & Sons. This book was released on 2015-09-14 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: A mathematical introduction to the theory and applications of logic and set theory with an emphasis on writing proofs Highlighting the applications and notations of basic mathematical concepts within the framework of logic and set theory, A First Course in Mathematical Logic and Set Theory introduces how logic is used to prepare and structure proofs and solve more complex problems. The book begins with propositional logic, including two-column proofs and truth table applications, followed by first-order logic, which provides the structure for writing mathematical proofs. Set theory is then introduced and serves as the basis for defining relations, functions, numbers, mathematical induction, ordinals, and cardinals. The book concludes with a primer on basic model theory with applications to abstract algebra. A First Course in Mathematical Logic and Set Theory also includes: Section exercises designed to show the interactions between topics and reinforce the presented ideas and concepts Numerous examples that illustrate theorems and employ basic concepts such as Euclid’s lemma, the Fibonacci sequence, and unique factorization Coverage of important theorems including the well-ordering theorem, completeness theorem, compactness theorem, as well as the theorems of Löwenheim–Skolem, Burali-Forti, Hartogs, Cantor–Schröder–Bernstein, and König An excellent textbook for students studying the foundations of mathematics and mathematical proofs, A First Course in Mathematical Logic and Set Theory is also appropriate for readers preparing for careers in mathematics education or computer science. In addition, the book is ideal for introductory courses on mathematical logic and/or set theory and appropriate for upper-undergraduate transition courses with rigorous mathematical reasoning involving algebra, number theory, or analysis.
Download or read book Notes on Logic and Set Theory written by P. T. Johnstone and published by Cambridge University Press. This book was released on 1987-10-08 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: A succinct introduction to mathematical logic and set theory, which together form the foundations for the rigorous development of mathematics. Suitable for all introductory mathematics undergraduates, Notes on Logic and Set Theory covers the basic concepts of logic: first-order logic, consistency, and the completeness theorem, before introducing the reader to the fundamentals of axiomatic set theory. Successive chapters examine the recursive functions, the axiom of choice, ordinal and cardinal arithmetic, and the incompleteness theorems. Dr. Johnstone has included numerous exercises designed to illustrate the key elements of the theory and to provide applications of basic logical concepts to other areas of mathematics.
Download or read book Elements of Set Theory written by Herbert B. Enderton and published by Academic Press. This book was released on 1977-05-23 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introductory undergraduate textbook in set theory. In mathematics these days, essentially everything is a set. Some knowledge of set theory is necessary part of the background everyone needs for further study of mathematics. It is also possible to study set theory for its own interest--it is a subject with intruiging results anout simple objects. This book starts with material that nobody can do without. There is no end to what can be learned of set theory, but here is a beginning.
Download or read book Set Theory written by Daniel W. Cunningham and published by Cambridge University Press. This book was released on 2016-07-18 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Set theory can be considered a unifying theory for mathematics. This book covers the fundamentals of the subject.
