Classic Set Theory

Author : D.C. Goldrei
Publisher : Routledge
Page : 296 pages
File Size : 40,5 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 : D.C. Goldrei
Publisher : Routledge
Page : 296 pages
File Size : 47,5 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 : 492 pages
File Size : 47,8 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 : 50,5 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 : Yiannis Moschovakis
Publisher : Springer Science & Business Media
Page : 280 pages
File Size : 44,8 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475741537

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Notes on Set Theory by Yiannis Moschovakis Pdf

What this book is about. The theory of sets is a vibrant, exciting math ematical theory, with its own basic notions, fundamental results and deep open problems, and with significant applications to other mathematical theories. At the same time, axiomatic set theory is often viewed as a foun dation ofmathematics: it is alleged that all mathematical objects are sets, and their properties can be derived from the relatively few and elegant axioms about sets. Nothing so simple-minded can be quite true, but there is little doubt that in standard, current mathematical practice, "making a notion precise" is essentially synonymous with "defining it in set theory. " Set theory is the official language of mathematics, just as mathematics is the official language of science. Like most authors of elementary, introductory books about sets, I have tried to do justice to both aspects of the subject. From straight set theory, these Notes cover the basic facts about "ab stract sets," including the Axiom of Choice, transfinite recursion, and car dinal and ordinal numbers. Somewhat less common is the inclusion of a chapter on "pointsets" which focuses on results of interest to analysts and introduces the reader to the Continuum Problem, central to set theory from the very beginning.

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 : Patrick Suppes
Publisher : Courier Corporation
Page : 265 pages
File Size : 46,5 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 Jech
Publisher : Marcel Dekker
Page : 264 pages
File Size : 55,7 Mb
Release : 1984
Category : Mathematics
ISBN : 0824785819

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Introduction to Set Theory by Karel Hrbacek,Thomas Jech Pdf

Author : Herbert B. Enderton
Publisher : Academic Press
Page : 279 pages
File Size : 52,7 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 : Charles C Pinter
Publisher : Courier Corporation
Page : 259 pages
File Size : 40,8 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 : Felix Hausdorff
Publisher : American Mathematical Soc.
Page : 352 pages
File Size : 46,7 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 : J.L. Krivine
Publisher : Springer Science & Business Media
Page : 108 pages
File Size : 40,5 Mb
Release : 2012-12-06
Category : Philosophy
ISBN : 9789401031448

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Introduction to Axiomatic Set Theory by J.L. Krivine Pdf

This book presents the classic relative consistency proofs in set theory that are obtained by the device of 'inner models'. Three examples of such models are investigated in Chapters VI, VII, and VIII; the most important of these, the class of constructible sets, leads to G6del's result that the axiom of choice and the continuum hypothesis are consistent with the rest of set theory [1]I. The text thus constitutes an introduction to the results of P. Cohen concerning the independence of these axioms [2], and to many other relative consistency proofs obtained later by Cohen's methods. Chapters I and II introduce the axioms of set theory, and develop such parts of the theory as are indispensable for every relative consistency proof; the method of recursive definition on the ordinals being an import ant case in point. Although, more or less deliberately, no proofs have been omitted, the development here will be found to require of the reader a certain facility in naive set theory and in the axiomatic method, such e as should be achieved, for example, in first year graduate work (2 cycle de mathernatiques).

Author : Paul J. Cohen
Publisher : Courier Corporation
Page : 196 pages
File Size : 43,5 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 : F. William Lawvere,Robert Rosebrugh
Publisher : Cambridge University Press
Page : 280 pages
File Size : 49,9 Mb
Release : 2003-01-27
Category : Mathematics
ISBN : 0521010608

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Sets for Mathematics by F. William Lawvere,Robert Rosebrugh Pdf

In this book, first published in 2003, categorical algebra is used to build a foundation for the study of geometry, analysis, and algebra.

Author : Moshe Machover
Publisher : Cambridge University Press
Page : 304 pages
File Size : 42,9 Mb
Release : 1996-05-23
Category : Mathematics
ISBN : 0521479983

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Set Theory, Logic and Their Limitations by Moshe Machover Pdf

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.