Classic Set Theory

Author : D.C. Goldrei
Publisher : Routledge
Page : 296 pages
File Size : 45,9 Mb
Release : 2017-09-06
Category : Mathematics
ISBN : 9781351460613

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Classic Set Theory by D.C. Goldrei Pdf

Designed for undergraduate students of set theory, Classic Set Theory presents a modern perspective of the classic work of Georg Cantor and Richard Dedekin and their immediate successors. This includes:The definition of the real numbers in terms of rational numbers and ultimately in terms of natural numbersDefining natural numbers in terms of setsThe potential paradoxes in set theoryThe Zermelo-Fraenkel axioms for set theoryThe axiom of choiceThe arithmetic of ordered setsCantor's two sorts of transfinite number - cardinals and ordinals - and the arithmetic of these.The book is designed for students studying on their own, without access to lecturers and other reading, along the lines of the internationally renowned courses produced by the Open University. There are thus a large number of exercises within the main body of the text designed to help students engage with the subject, many of which have full teaching solutions. In addition, there are a number of exercises without answers so students studying under the guidance of a tutor may be assessed.Classic Set Theory gives students sufficient grounding in a rigorous approach to the revolutionary results of set theory as well as pleasure in being able to tackle significant problems that arise from the theory.

Author : Peter Komjath,Vilmos Totik
Publisher : Springer Science & Business Media
Page : 516 pages
File Size : 44,6 Mb
Release : 2006-11-22
Category : Mathematics
ISBN : 9780387362199

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Problems and Theorems in Classical Set Theory by Peter Komjath,Vilmos Totik Pdf

This volume contains a variety of problems from classical set theory and represents the first comprehensive collection of such problems. Many of these problems are also related to other fields of mathematics, including algebra, combinatorics, topology and real analysis. Rather than using drill exercises, most problems are challenging and require work, wit, and inspiration. They vary in difficulty, and are organized in such a way that earlier problems help in the solution of later ones. For many of the problems, the authors also trace the history of the problems and then provide proper reference at the end of the solution.

Author : Alexander Kechris
Publisher : Springer Science & Business Media
Page : 419 pages
File Size : 47,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461241904

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Classical Descriptive Set Theory by Alexander Kechris Pdf

Descriptive set theory has been one of the main areas of research in set theory for almost a century. This text presents a largely balanced approach to the subject, which combines many elements of the different traditions. It includes a wide variety of examples, more than 400 exercises, and applications, in order to illustrate the general concepts and results of the theory.

Author : Paul Richard Halmos
Publisher : Unknown
Page : 122 pages
File Size : 54,5 Mb
Release : 1960
Category : Mathematics
ISBN : UOM:39015006570702

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Naive Set Theory by Paul Richard Halmos Pdf

From the Reviews: .,."He (the author) uses the language and notation of ordinary informal mathematics to state the basic set-theoretic facts which a beginning student of advanced mathematics needs to know. ...Because of the informal method of presentation, the book is eminently suited for use as a textbook or for self-study. The reader should derive from this volume a maximum of understanding of the theorems of set theory and of their basic importance in the study of mathematics." Philosophy and Phenomenological Research

Author : Herbert B. Enderton
Publisher : Academic Press
Page : 279 pages
File Size : 46,8 Mb
Release : 1977-05-23
Category : Mathematics
ISBN : 9780080570426

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Elements of Set Theory by Herbert B. Enderton Pdf

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.

Author : Patrick Suppes
Publisher : Courier Corporation
Page : 265 pages
File Size : 45,8 Mb
Release : 2012-05-04
Category : Mathematics
ISBN : 9780486136875

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Axiomatic Set Theory by Patrick Suppes Pdf

Geared toward upper-level undergraduates and graduate students, this treatment examines the basic paradoxes and history of set theory and advanced topics such as relations and functions, equipollence, more. 1960 edition.

Author : Karel Hrbacek,Thomas J. Jech
Publisher : Unknown
Page : 272 pages
File Size : 55,6 Mb
Release : 1984
Category : Set theory
ISBN : UOM:39076000787080

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Introduction to Set Theory by Karel Hrbacek,Thomas J. Jech Pdf

Author : Charles C Pinter
Publisher : Courier Corporation
Page : 259 pages
File Size : 44,5 Mb
Release : 2014-07-23
Category : Mathematics
ISBN : 9780486497082

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A Book of Set Theory by Charles C Pinter Pdf

"This accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. Each definition is accompanied by commentary that motivates and explains new concepts. A historical introduction is followed by discussions of classes and sets, functions, natural and cardinal numbers, the arithmetic of ordinal numbers, and related topics. 1971 edition with new material by the author"--

Author : Paul J. Cohen
Publisher : Courier Corporation
Page : 196 pages
File Size : 42,6 Mb
Release : 2008-12-09
Category : Mathematics
ISBN : 9780486469218

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Set Theory and the Continuum Hypothesis by Paul J. Cohen Pdf

This exploration of a notorious mathematical problem is the work of the man who discovered the solution. Written by an award-winning professor at Stanford University, it employs intuitive explanations as well as detailed mathematical proofs in a self-contained treatment. This unique text and reference is suitable for students and professionals. 1966 edition. Copyright renewed 1994.

Author : Felix Hausdorff
Publisher : American Mathematical Soc.
Page : 352 pages
File Size : 51,9 Mb
Release : 2021-08-24
Category : Education
ISBN : 9781470464943

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Set Theory by Felix Hausdorff Pdf

This work is a translation into English of the Third Edition of the classic German language work Mengenlehre by Felix Hausdorff published in 1937. From the Preface (1937): “The present book has as its purpose an exposition of the most important theorems of the theory of sets, along with complete proofs, so that the reader should not find it necessary to go outside this book for supplementary details while, on the other hand, the book should enable him to undertake a more detailed study of the voluminous literature on the subject. The book does not presuppose any mathematical knowledge beyond the differential and integral calculus, but it does require a certain maturity in abstract reasoning; qualified college seniors and first year graduate students should have no difficulty in making the material their own … The mathematician will … find in this book some things that will be new to him, at least as regards formal presentation and, in particular, as regards the strengthening of theorems, the simplification of proofs, and the removal of unnecessary hypotheses.”

Author : Douglas Cenzer,Jean Larson,Christopher Porter,Jindrich Zapletal
Publisher : World Scientific
Page : 222 pages
File Size : 49,9 Mb
Release : 2020-04-04
Category : Mathematics
ISBN : 9789811201943

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Set Theory And Foundations Of Mathematics: An Introduction To Mathematical Logic - Volume I: Set Theory by Douglas Cenzer,Jean Larson,Christopher Porter,Jindrich Zapletal Pdf

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.

Author : Michael Potter
Publisher : Clarendon Press
Page : 362 pages
File Size : 51,5 Mb
Release : 2004-01-15
Category : Philosophy
ISBN : 9780191556432

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Set Theory and its Philosophy by Michael Potter Pdf

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 : Joseph Breuer
Publisher : Courier Corporation
Page : 130 pages
File Size : 53,6 Mb
Release : 2012-08-09
Category : Mathematics
ISBN : 9780486154879

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Introduction to the Theory of Sets by Joseph Breuer Pdf

This undergraduate text develops its subject through observations of the physical world, covering finite sets, cardinal numbers, infinite cardinals, and ordinals. Includes exercises with answers. 1958 edition.

Author : Irving Kaplansky
Publisher : American Mathematical Society
Page : 140 pages
File Size : 49,7 Mb
Release : 2020-09-10
Category : Mathematics
ISBN : 9781470463847

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Set Theory and Metric Spaces by Irving Kaplansky Pdf

This is a book that could profitably be read by many graduate students or by seniors in strong major programs … has a number of good features. There are many informal comments scattered between the formal development of theorems and these are done in a light and pleasant style. … There is a complete proof of the equivalence of the axiom of choice, Zorn's Lemma, and well-ordering, as well as a discussion of the use of these concepts. There is also an interesting discussion of the continuum problem … The presentation of metric spaces before topological spaces … should be welcomed by most students, since metric spaces are much closer to the ideas of Euclidean spaces with which they are already familiar. —Canadian Mathematical Bulletin Kaplansky has a well-deserved reputation for his expository talents. The selection of topics is excellent. — Lance Small, UC San Diego This book is based on notes from a course on set theory and metric spaces taught by Edwin Spanier, and also incorporates with his permission numerous exercises from those notes. The volume includes an Appendix that helps bridge the gap between metric and topological spaces, a Selected Bibliography, and an Index.

Author : Valeriy K. Zakharov,Timofey V. Rodionov
Publisher : Walter de Gruyter GmbH & Co KG
Page : 446 pages
File Size : 49,9 Mb
Release : 2018-02-05
Category : Mathematics
ISBN : 9783110550948

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Fundamentals of Set and Number Theory by Valeriy K. Zakharov,Timofey V. Rodionov Pdf

This comprehensive two-volume work is devoted to the most general beginnings of mathematics. It goes back to Hausdorff’s classic Set Theory (2nd ed., 1927), where set theory and the theory of functions were expounded as the fundamental parts of mathematics in such a way that there was no need for references to other sources. Along the lines of Hausdorff’s initial work (1st ed., 1914), measure and integration theory is also included here as the third fundamental part of contemporary mathematics.The material about sets and numbers is placed in Volume 1 and the material about functions and measures is placed in Volume 2. Contents Fundamentals of the theory of classes, sets, and numbers Characterization of all natural models of Neumann – Bernays – Godel and Zermelo – Fraenkel set theories Local theory of sets as a foundation for category theory and its connection with the Zermelo – Fraenkel set theory Compactness theorem for generalized second-order language