## Notes On Set Theory

**Author**: Yiannis Moschovakis

**Editor:**Springer Science & Business Media

**ISBN:**1475741537

**Size**: 10,10 MB

**Format:**PDF, ePub, Docs

**Read:**519

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.

## Notes On Logic And Set Theory

**Author**: P. T. Johnstone

**Editor:**Cambridge University Press

**ISBN:**9780521336925

**Size**: 10,65 MB

**Format:**PDF, ePub

**Read:**189

This short textbook provides a succinct introduction to mathematical logic and set theory, which together form the foundations for the rigorous development of mathematics. It will be suitable for all mathematics undergraduates coming to the subject for the first time. The book is based on lectures given at the University of Cambridge and 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. There are also chapters on 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. Consequently the book, while making an attractive first textbook for those who plan to specialise in logic, will be particularly valuable for mathematics and computer scientists whose primary interests lie elsewhere.

## Notes On Set Theory And The Bare Bones Of Mathematical Logic

**Author**: Warren Brisley

**Editor:**

**ISBN:**9780725904234

**Size**: 19,98 MB

**Format:**PDF, ePub, Mobi

**Read:**468

## Elements Of Set Theory

**Author**: Herbert B. Enderton

**Editor:**Gulf Professional Publishing

**ISBN:**0122384407

**Size**: 19,96 MB

**Format:**PDF, Kindle

**Read:**850

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.

## An Outline Of Set Theory

**Author**: James M. Henle

**Editor:**Courier Corporation

**ISBN:**0486453375

**Size**: 16,49 MB

**Format:**PDF, ePub, Docs

**Read:**422

An innovative problem-oriented introduction to set theory, this volume is intended for undergraduate courses in which students work in groups on projects and present their solutions to the class. The three-part treatment consists of problems, hints for their solutions, and complete answers. 1986 edition.

## The Joy Of Sets

**Author**: Keith Devlin

**Editor:**Springer Science & Business Media

**ISBN:**9780387940946

**Size**: 16,76 MB

**Format:**PDF, ePub, Mobi

**Read:**926

This text covers the parts of contemporary set theory relevant to other areas of pure mathematics. After a review of "naïve" set theory, it develops the Zermelo-Fraenkel axioms of the theory before discussing the ordinal and cardinal numbers. It then delves into contemporary set theory, covering such topics as the Borel hierarchy and Lebesgue measure. A final chapter presents an alternative conception of set theory useful in computer science.

## A Book Of Set Theory

**Author**: Charles C Pinter

**Editor:**Courier Corporation

**ISBN:**0486497089

**Size**: 16,56 MB

**Format:**PDF, ePub

**Read:**207

"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"--

## Basic Set Theory

**Author**: Nikolai Konstantinovich Vereshchagin

**Editor:**American Mathematical Soc.

**ISBN:**0821827316

**Size**: 11,11 MB

**Format:**PDF, Kindle

**Read:**123

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 dedicated treatment. This book provides just that in the form of 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.

## Surveys In Set Theory

**Author**: A. R. D. Mathias

**Editor:**Cambridge University Press

**ISBN:**0521277337

**Size**: 18,23 MB

**Format:**PDF, Kindle

**Read:**425

This book comprises five expository articles and two research papers on topics of current interest in set theory and the foundations of mathematics. Articles by Baumgartner and Devlin introduce the reader to proper forcing. This is a development by Saharon Shelah of Cohen's method which has led to solutions of problems that resisted attack by forcing methods as originally developed in the 1960s. The article by Guaspari is an introduction to descriptive set theory, a subject that has developed dramatically in the last few years. Articles by Kanamori and Stanley discuss one of the most difficult concepts in contemporary set theory, that of the morass, first created by Ronald Jensen in 1971 to solve the gap-two conjecture in model theory, assuming Gödel's axiom of constructibility. The papers by Prikry and Shelah complete the volume by giving the reader the flavour of contemporary research in set theory. This book will be of interest to graduate students and research workers in set theory and mathematical logic.

## Set Theory For The Working Mathematician

**Author**: Krzysztof Ciesielski

**Editor:**Cambridge University Press

**ISBN:**9780521594653

**Size**: 14,25 MB

**Format:**PDF, Kindle

**Read:**252

Presents those methods of modern set theory most applicable to other areas of pure mathematics.