Notes On Set Theory

Author : Yiannis Moschovakis
Publisher : Springer Science & Business Media
Page : 280 pages
File Size : 51,8 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 : Herbert B. Enderton
Publisher : Academic Press
Page : 279 pages
File Size : 51,5 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 : P. T. Johnstone
Publisher : Cambridge University Press
Page : 128 pages
File Size : 54,6 Mb
Release : 1987-10-08
Category : Mathematics
ISBN : 0521335027

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Notes on Logic and Set Theory by P. T. Johnstone Pdf

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.

Author : Charles C Pinter
Publisher : Courier Corporation
Page : 259 pages
File Size : 54,9 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 : Norman T. Hamilton,Joseph Landin
Publisher : Courier Dover Publications
Page : 288 pages
File Size : 41,6 Mb
Release : 2018-05-16
Category : Mathematics
ISBN : 9780486830476

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Set Theory: The Structure of Arithmetic by Norman T. Hamilton,Joseph Landin Pdf

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.

Author : Robert R. Stoll
Publisher : Courier Corporation
Page : 512 pages
File Size : 42,8 Mb
Release : 2012-05-23
Category : Mathematics
ISBN : 9780486139647

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Set Theory and Logic by Robert R. Stoll Pdf

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.

Author : Thomas J. Jech
Publisher : Lecture Notes in Mathematics
Page : 156 pages
File Size : 42,8 Mb
Release : 1971-09-23
Category : Mathematics
ISBN : STANFORD:36105030773944

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Lectures in Set Theory by Thomas J. Jech Pdf

Author : D.C. Goldrei
Publisher : Routledge
Page : 296 pages
File Size : 52,6 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 : Lorenz J. Halbeisen
Publisher : Springer
Page : 594 pages
File Size : 40,8 Mb
Release : 2017-12-20
Category : Mathematics
ISBN : 9783319602318

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Combinatorial Set Theory by Lorenz J. Halbeisen Pdf

This book, now in a thoroughly revised second edition, provides a comprehensive and accessible introduction to modern set theory. Following an overview of basic notions in combinatorics and first-order logic, the author outlines the main topics of classical set theory in the second part, including Ramsey theory and the axiom of choice. The revised edition contains new permutation models and recent results in set theory without the axiom of choice. The third part explains the sophisticated technique of forcing in great detail, now including a separate chapter on Suslin’s problem. The technique is used to show that certain statements are neither provable nor disprovable from the axioms of set theory. In the final part, some topics of classical set theory are revisited and further developed in light of forcing, with new chapters on Sacks Forcing and Shelah’s astonishing construction of a model with finitely many Ramsey ultrafilters. 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 and historical remarks at the end of each chapter, this book is suitable for self-study.

Author : Daniel W. Cunningham
Publisher : Cambridge University Press
Page : 265 pages
File Size : 44,7 Mb
Release : 2016-07-18
Category : Mathematics
ISBN : 9781107120327

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Set Theory by Daniel W. Cunningham Pdf

Set theory can be considered a unifying theory for mathematics. This book covers the fundamentals of the subject.

Author : Peter Komjath,Vilmos Totik
Publisher : Springer Science & Business Media
Page : 492 pages
File Size : 42,7 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 : 48,6 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 : Michael Potter
Publisher : Clarendon Press
Page : 362 pages
File Size : 45,9 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 : Patrick Suppes
Publisher : Courier Corporation
Page : 265 pages
File Size : 41,9 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 : 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