Introduction To Set Theory
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Set Theory An Introduction To Independence Proofs
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Author : K. Kunen
language : en
Publisher: Elsevier
Release Date : 2014-06-28
Set Theory An Introduction To Independence Proofs written by K. Kunen and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-28 with Mathematics categories.
Studies in Logic and the Foundations of Mathematics, Volume 102: Set Theory: An Introduction to Independence Proofs offers an introduction to relative consistency proofs in axiomatic set theory, including combinatorics, sets, trees, and forcing. The book first tackles the foundations of set theory and infinitary combinatorics. Discussions focus on the Suslin problem, Martin's axiom, almost disjoint and quasi-disjoint sets, trees, extensionality and comprehension, relations, functions, and well-ordering, ordinals, cardinals, and real numbers. The manuscript then ponders on well-founded sets and easy consistency proofs, including relativization, absoluteness, reflection theorems, properties of well-founded sets, and induction and recursion on well-founded relations. The publication examines constructible sets, forcing, and iterated forcing. Topics include Easton forcing, general iterated forcing, Cohen model, forcing with partial functions of larger cardinality, forcing with finite partial functions, and general extensions. The manuscript is a dependable source of information for mathematicians and researchers interested in set theory.
Set Theory And Foundations Of Mathematics An Introduction To Mathematical Logic Volume I Set Theory
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Author : Douglas Cenzer
language : en
Publisher: World Scientific
Release Date : 2020-04-04
Set Theory And Foundations Of Mathematics An Introduction To Mathematical Logic Volume I Set Theory written by Douglas Cenzer and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-04 with Mathematics categories.
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.
Set Theory
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Author : Abhijit Dasgupta
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-11
Set Theory written by Abhijit Dasgupta 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 2013-12-11 with Mathematics categories.
What is a number? What is infinity? What is continuity? What is order? Answers to these fundamental questions obtained by late nineteenth-century mathematicians such as Dedekind and Cantor gave birth to set theory. This textbook presents classical set theory in an intuitive but concrete manner. To allow flexibility of topic selection in courses, the book is organized into four relatively independent parts with distinct mathematical flavors. Part I begins with the Dedekind–Peano axioms and ends with the construction of the real numbers. The core Cantor–Dedekind theory of cardinals, orders, and ordinals appears in Part II. Part III focuses on the real continuum. Finally, foundational issues and formal axioms are introduced in Part IV. Each part ends with a postscript chapter discussing topics beyond the scope of the main text, ranging from philosophical remarks to glimpses into landmark results of modern set theory such as the resolution of Lusin's problems on projective sets using determinacy of infinite games and large cardinals. Separating the metamathematical issues into an optional fourth part at the end makes this textbook suitable for students interested in any field of mathematics, not just for those planning to specialize in logic or foundations. There is enough material in the text for a year-long course at the upper-undergraduate level. For shorter one-semester or one-quarter courses, a variety of arrangements of topics are possible. The book will be a useful resource for both experts working in a relevant or adjacent area and beginners wanting to learn set theory via self-study.
Introduction To Set Theory Third Edition Revised And Expanded
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Author : Karel Hrbacek
language : en
Publisher: CRC Press
Release Date : 1999-06-22
Introduction To Set Theory Third Edition Revised And Expanded written by Karel Hrbacek and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-06-22 with Mathematics categories.
Thoroughly revised, updated, expanded, and reorganized to serve as a primary text for mathematics courses, Introduction to Set Theory, Third Edition covers the basics: relations, functions, orderings, finite, countable, and uncountable sets, and cardinal and ordinal numbers. It also provides five additional self-contained chapters, consolidates the material on real numbers into a single updated chapter affording flexibility in course design, supplies end-of-section problems, with hints, of varying degrees of difficulty, includes new material on normal forms and Goodstein sequences, and adds important recent ideas including filters, ultrafilters, closed unbounded and stationary sets, and partitions.
Set Theory An Introduction
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Author : Robert L. Vaught
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-08-28
Set Theory An Introduction written by Robert L. Vaught 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 2001-08-28 with Mathematics categories.
By its nature, set theory does not depend on any previous mathematical knowl edge. Hence, an individual wanting to read this book can best find out if he is ready to do so by trying to read the first ten or twenty pages of Chapter 1. As a textbook, the book can serve for a course at the junior or senior level. If a course covers only some of the chapters, the author hopes that the student will read the rest himself in the next year or two. Set theory has always been a sub ject which people find pleasant to study at least partly by themselves. Chapters 1-7, or perhaps 1-8, present the core of the subject. (Chapter 8 is a short, easy discussion of the axiom of regularity). Even a hurried course should try to cover most of this core (of which more is said below). Chapter 9 presents the logic needed for a fully axiomatic set th~ory and especially for independence or consistency results. Chapter 10 gives von Neumann's proof of the relative consistency of the regularity axiom and three similar related results. Von Neumann's 'inner model' proof is easy to grasp and yet it prepares one for the famous and more difficult work of GOdel and Cohen, which are the main topics of any book or course in set theory at the next level.
Introduction To Set Theory
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Author : A. K. Sharma
language : en
Publisher: Discovery Publishing House
Release Date : 2010
Introduction To Set Theory written by A. K. Sharma and has been published by Discovery Publishing House this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Set theory categories.
This book Introduction to Set Theory is very important in the field of modern algebra. It is very important to study this book to study modern mathematics. This book contain preliminary Notation, Sets, Subsets, Mapping Function and Relation. This book is useful to the students of under graduate, post graduate students and the candidate appearing in various competitions like pre Engineering/I.A.S/ P.C.S. etc. Contents: Preliminary Notation, Relations, Product or Composite of Mapping, Mapping or Functions
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 And Its Philosophy
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Author : Michael Potter
language : en
Publisher: Clarendon Press
Release Date : 2004-01-15
Set Theory And Its Philosophy written by Michael Potter and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-15 with Philosophy categories.
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.
Set Theory For Pre Beginners
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Author : Steve Warner
language : en
Publisher:
Release Date : 2019-12-28
Set Theory For Pre Beginners written by Steve Warner and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-28 with categories.
Set Theory for Pre-BeginnersSet Theory for Pre-Beginners consists of a series of lessons in set theory. The 8 lessons in this book cover elementary material from this subject. A "pre-beginner" is a math student that is ready to start learning some more advanced mathematics, but is not quite ready to dive into proofwriting. Set Theory for Pre-Beginners is perfect for students wishing to begin learning advanced mathematics, but that are not quite ready to start writing proofs. high school teachers that want to expose their students to the ideas of advanced mathematics without getting into mathematical rigor. professors that wish to introduce higher mathematics to non-stem majors. The material in this set theory book includes: 8 lessons in 8 subject areas. Examples and exercises throughout each lesson. A problem set after each lesson arranged by difficulty level. A complete solution guide is included as a downloadable PDF file. Pure Math Pre-Beginner Book Table Of Contents (Selected) Here's a selection from the table of contents: Introduction Lesson 1 - Sets and Subsets Lesson 2 - Operations on Sets Lesson 3 - Relations Lesson 4 - Equivalence Relations and Partitions Lesson 5 - Functions Lesson 6 - Equinumerosity Lesson 7 - Logic and Axioms Lesson 8 - Ordinals and Cardinals
Philosophical Introduction To Set Theory
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Author : Stephen Pollard
language : en
Publisher: Courier Dover Publications
Release Date : 2015-07-15
Philosophical Introduction To Set Theory written by Stephen Pollard and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-15 with Mathematics categories.
This unique approach maintains that set theory is the primary mechanism for ideological and theoretical unification in modern mathematics, and its technically informed discussion covers a variety of philosophical issues. 1990 edition.