Elements Of Set Theory
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Elements Of Set Theory
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Author : Herbert B. Enderton
language : en
Publisher: Gulf Professional Publishing
Release Date : 1977-04-28
Elements Of Set Theory written by Herbert B. Enderton and has been published by Gulf Professional Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977-04-28 with Mathematics categories.
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.
Theory Of Sets
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Author : N. Bourbaki
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Theory Of Sets written by N. Bourbaki and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
This is a softcover reprint of the English translation of 1968 of N. Bourbaki's, Thorie des Ensembles (1970).
Elements Of Set Theory
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Author :
language : en
Publisher:
Release Date : 2006
Elements Of Set Theory written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.
Set Theory
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Author : Robert André
language : en
Publisher: CRC Press
Release Date : 2025-04-21
Set Theory written by Robert André and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-21 with Mathematics categories.
Contemporary students of mathematics differ considerably from those of half a century ago. In spite of this, many textbooks written decades ago, and now considered to be “classics”, are still prescribed for students today. These texts are not suitable for today’s students. This text is meant for and written to today’s mathematics students. Set theory is a pure mathematics endeavor in the sense that it seems to have no immediate applications; yet the knowledge and skills developed in such a course can easily branch out to various fields of both pure mathematics and applied mathematics. Rather than transforming the reader into a practicing mathematician, this book is more designed to initiate the reader to what may be called “mathematical thinking” while developing knowledge about foundations of modern mathematics. Without this insight, becoming a practicing mathematician is much more daunting. The main objective is twofold. The students will develop some fundamental understanding of the foundations of mathematics and elements of set theory, in general. In the process, the student will develop skills in proving simple mathematical statements with “mathematical rigor”. Carefully presented detailed proofs and rigorous chains of logical arguments will guide the students from the fundamental ZFC-axioms and definitions to show why a basic mathematical statement must hold true. The student will recognize the role played by each fundamental axiom in development of modern mathematics. The student will learn to distinguish between a correct mathematical proof and an erroneous one. The subject matter is presented while bypassing the complexities encountered when using formal logic.
Basic Set Theory
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Author : Nikolai Konstantinovich Vereshchagin
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Basic Set Theory written by Nikolai Konstantinovich Vereshchagin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
The main notions of set theory (cardinals, ordinals, transfinite induction) are fundamental to all mathematicians, not only to those who specialize in mathematical logic or set-theoretic topology. Basic set theory is generally given a brief overview in courses on analysis, algebra, or topology, even though it is sufficiently important, interesting, and simple to merit its own leisurely treatment. This book provides just that: a leisurely exposition for a diversified audience. It is suitable for a broad range of readers, from undergraduate students to professional mathematicians who want to finally find out what transfinite induction is and why it is always replaced by Zorn's Lemma. The text introduces all main subjects of ``naive'' (nonaxiomatic) set theory: functions, cardinalities, ordered and well-ordered sets, transfinite induction and its applications, ordinals, and operations on ordinals. Included are discussions and proofs of the Cantor-Bernstein Theorem, Cantor's diagonal method, Zorn's Lemma, Zermelo's Theorem, and Hamel bases. With over 150 problems, the book is a complete and accessible introduction to the subject.
Set Theory
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Author : Andras Hajnal
language : en
Publisher: Cambridge University Press
Release Date : 1999-11-11
Set Theory written by Andras Hajnal and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-11-11 with Mathematics categories.
This is a classic introduction to set theory in three parts. The first part gives a general introduction to set theory, suitable for undergraduates; complete proofs are given and no background in logic is required. Exercises are included, and the more difficult ones are supplied with hints. An appendix to the first part gives a more formal foundation to axiomatic set theory, supplementing the intuitive introduction given in the first part. The final part gives an introduction to modern tools of combinatorial set theory. This part contains enough material for a graduate course of one or two semesters. The subjects discussed include stationary sets, delta systems, partition relations, set mappings, measurable and real-valued measurable cardinals. Two sections give an introduction to modern results on exponentiation of singular cardinals, and certain deeper aspects of the topics are developed in advanced problems.
Combinatorial Set Theory
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Author : Lorenz J. Halbeisen
language : en
Publisher: Springer Nature
Release Date : 2025-05-26
Combinatorial Set Theory written by Lorenz J. Halbeisen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-26 with Mathematics categories.
This book, now in a revised and extended third edition, provides a comprehensive and accessible introduction to modern axiomatic set theory. After an overview of basic notions in combinatorics and first-order logic, and discussing in great detail the axioms of set theory, the author outlines in the second part the main topics of classical set theory, including Ramsey theory and the axiom of choice. As an application of the axiom of choice, a complete proof of Robinson's construction for doubling a ball by dividing it into only five parts is given. For the new edition, the chapter on permutation models has been extended, and recent results in set theory without the axiom of choice and about cardinal characteristics have been added. The third part explains the sophisticated technique of forcing from scratch, now including more details about iterated forcing. The technique is then used to show that certain statements are neither provable nor disprovable from the axioms of set theory. In particular, it is shown that both Martin's Axiom and Suslin's Hypothesis are independent of the axioms of set theory. The final part, with a new chapter on Laver forcing, is mainly concerned with consistency results obtained by iterations of forcing notions such as Cohen forcing, Sacks forcing, and Mathias forcing. The part begins with an extended chapter on countable support iterations of proper forcing notions, now also including proofs of some preservation theorems such as preservation of properness and of certain ultrafilters. In the following chapters, various consistency results concerning possible relations between cardinal characteristics and the existence of Ramsey ultrafilters are presented. For example, a detailed proof of Shelah’s astonishing construction of a model with finitely many Ramsey ultrafilters is given. Written for graduate students in axiomatic set theory, Combinatorial Set Theory will appeal to all researchers interested in the foundations of mathematics. With extensive reference lists, historical remarks, and related results at the end of the chapters, this book is also suitable for self-study.
Applied Set Theory And Logic
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Author : John-Michael Kuczynski
language : en
Publisher: John-Michael Kuczynski
Release Date : 2025-06-12
Applied Set Theory And Logic written by John-Michael Kuczynski and has been published by John-Michael Kuczynski this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-12 with Philosophy categories.
Applied Set Theory and Logic is a comprehensive guide to the core principles of set theory and mathematical logic, with an emphasis on real-world applications in computer science, engineering, and digital systems. Bridging rigorous theoretical foundations with practical examples, the book explores topics ranging from propositional calculus and predicate logic to modal logic, database systems, circuit verification, and algorithm design. Through hundreds of worked examples and exercises, readers learn to apply logical reasoning to concrete problems in programming, software verification, hardware design, and information systems. Advanced topics include modal logic, recursion, transitivity, Von Neumann and Zermelo ordinals, Boolean algebra, and formal proof techniques. Each chapter highlights the relevance of logic and set theory to contemporary computational systems and digital technologies. Suitable for students, engineers, computer scientists, and researchers, Applied Set Theory and Logic serves both as a theoretical reference and a practical guide to the logical structures that underlie modern technology.
Proofs And Logic A Comprehensive Guide To Mathematical Reasoning
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Author : Pasquale De Marco
language : en
Publisher: Pasquale De Marco
Release Date : 2025-03-15
Proofs And Logic A Comprehensive Guide To Mathematical Reasoning written by Pasquale De Marco and has been published by Pasquale De Marco this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-15 with Mathematics categories.
In the realm of mathematics, proofs stand as the gatekeepers of truth, ensuring that mathematical statements are not mere assertions but logical consequences of established axioms and definitions. "Proofs and Logic: A Comprehensive Guide to Mathematical Reasoning" is your gateway to mastering the art of mathematical proof construction. This comprehensive book is meticulously crafted to empower you with the skills and techniques necessary to navigate the intricate world of mathematical arguments. Whether you are a student seeking to excel in your studies, a teacher aiming to inspire your students, or a professional mathematician seeking to expand your knowledge, this book is your essential companion. With crystal-clear explanations, engaging examples, and thought-provoking exercises, this book takes you on a journey through the diverse landscape of proofs. From direct proofs that establish the truth of a statement through a sequence of logical steps to proofs by contradiction that reveal the absurdity of a statement's negation, you will gain a deep understanding of the various methods of proof construction. Beyond the realm of proofs, this book delves into the foundations of logic, set theory, propositional logic, and predicate logic, providing you with a solid grasp of the formal structure of mathematical statements. With this knowledge, you will be able to analyze and evaluate mathematical arguments with precision and rigor. As you progress through this book, you will not only develop a profound appreciation for the beauty and elegance of mathematical proofs but also cultivate a valuable skill set that will serve you well in your academic and professional endeavors. Whether you aspire to pursue a career in mathematics, science, engineering, or any field that values logical reasoning, this book is your indispensable guide. Join us on this intellectual adventure as we unlock the power of logical reasoning and embark on a journey into the fascinating world of mathematical proofs. "Proofs and Logic" is more than just a book; it is an invitation to embark on a transformative learning experience that will reshape your understanding of mathematics and empower you to tackle complex problems with confidence. If you like this book, write a review!
Badiou S Being And Event And The Mathematics Of Set Theory
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Author : Burhanuddin Baki
language : en
Publisher: Bloomsbury Publishing
Release Date : 2014-11-20
Badiou S Being And Event And The Mathematics Of Set Theory written by Burhanuddin Baki and has been published by Bloomsbury Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-20 with Philosophy categories.
Alain Badiou's Being and Event continues to impact philosophical investigations into the question of Being. By exploring the central role set theory plays in this influential work, Burhanuddin Baki presents the first extended study of Badiou's use of mathematics in Being and Event. Adopting a clear, straightforward approach, Baki gathers together and explains the technical details of the relevant high-level mathematics in Being and Event. He examines Badiou's philosophical framework in close detail, showing exactly how it is 'conditioned' by the technical mathematics. Clarifying the relevant details of Badiou's mathematics, Baki looks at the four core topics Badiou employs from set theory: the formal axiomatic system of ZFC; cardinal and ordinal numbers; Kurt Gödel's concept of constructability; and Cohen's technique of forcing. Baki then rebuilds Badiou's philosophical meditations in relation to their conditioning by the mathematics, paying particular attention to Cohen's forcing, which informs Badiou's analysis of the event. Providing valuable insights into Badiou's philosophy of mathematics, Badiou's Being and Event and the Mathematics of Set Theory offers an excellent commentary and a new reading of Badiou's most complex and important work.