Basic Set Theory

Author : Nikolai Konstantinovich Vereshchagin,Alexander Shen
Publisher : American Mathematical Soc.
Page : 130 pages
File Size : 42,7 Mb
Release : 2002
Category : Set theory
ISBN : 9780821827314

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Basic Set Theory by Nikolai Konstantinovich Vereshchagin,Alexander Shen Pdf

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.

Author : Azriel Levy
Publisher : Courier Corporation
Page : 418 pages
File Size : 41,8 Mb
Release : 2012-06-11
Category : Mathematics
ISBN : 9780486150734

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Basic Set Theory by Azriel Levy Pdf

Although this book deals with basic set theory (in general, it stops short of areas where model-theoretic methods are used) on a rather advanced level, it does it at an unhurried pace. This enables the author to pay close attention to interesting and important aspects of the topic that might otherwise be skipped over. Written for upper-level undergraduate and graduate students, the book is divided into two parts. The first covers pure set theory, including the basic notions, order and well-foundedness, cardinal numbers, the ordinals, and the axiom of choice and some of its consequences. The second part deals with applications and advanced topics, among them a review of point set topology, the real spaces, Boolean algebras, and infinite combinatorics and large cardinals. A helpful appendix deals with eliminability and conservation theorems, while numerous exercises supply additional information on the subject matter and help students test their grasp of the material. 1979 edition. 20 figures.

Author : Paul Richard Halmos
Publisher : Unknown
Page : 122 pages
File Size : 53,9 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 : Azriel Levy
Publisher : Springer Verlag
Page : 391 pages
File Size : 54,5 Mb
Release : 1979
Category : Mathematics
ISBN : 0387084177

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Basic Set Theory by Azriel Levy Pdf

Author : Yiannis Moschovakis
Publisher : Springer Science & Business Media
Page : 280 pages
File Size : 51,6 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 : Daniel W. Cunningham
Publisher : Cambridge University Press
Page : 265 pages
File Size : 53,8 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 : Richard Kohar
Publisher : World Scientific Publishing Company
Page : 732 pages
File Size : 49,6 Mb
Release : 2016-06-15
Category : Mathematics
ISBN : 9789814730419

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Basic Discrete Mathematics by Richard Kohar Pdf

This lively introductory text exposes the student in the humanities to the world of discrete mathematics. A problem-solving based approach grounded in the ideas of George Pólya are at the heart of this book. Students learn to handle and solve new problems on their own. A straightforward, clear writing style and well-crafted examples with diagrams invite the students to develop into precise and critical thinkers. Particular attention has been given to the material that some students find challenging, such as proofs. This book illustrates how to spot invalid arguments, to enumerate possibilities, and to construct probabilities. It also presents case studies to students about the possible detrimental effects of ignoring these basic principles. The book is invaluable for a discrete and finite mathematics course at the freshman undergraduate level or for self-study since there are full solutions to the exercises in an appendix. "Written with clarity, humor and relevant real-world examples, Basic Discrete Mathematics is a wonderful introduction to discrete mathematical reasoning."- Arthur Benjamin, Professor of Mathematics at Harvey Mudd College, and author of The Magic of Math

Author : Herbert B. Enderton
Publisher : Academic Press
Page : 279 pages
File Size : 54,8 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 : Michael Potter
Publisher : Clarendon Press
Page : 362 pages
File Size : 50,9 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 : Moshe Machover
Publisher : Cambridge University Press
Page : 304 pages
File Size : 40,5 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.

Author : Robert R. Stoll
Publisher : Courier Corporation
Page : 512 pages
File Size : 49,5 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 : Erich Kamke
Publisher : Courier Corporation
Page : 164 pages
File Size : 41,8 Mb
Release : 1950-01-01
Category : Mathematics
ISBN : 0486601412

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Theory of Sets by Erich Kamke Pdf

Introductory treatment emphasizes fundamentals, covering rudiments; arbitrary sets and their cardinal numbers; ordered sets and their ordered types; and well-ordered sets and their ordinal numbers. "Exceptionally well written." ? School Science and Mathematics.

Author : Charles C Pinter
Publisher : Courier Corporation
Page : 259 pages
File Size : 40,6 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 : Judith Roitman
Publisher : John Wiley & Sons
Page : 188 pages
File Size : 54,7 Mb
Release : 1990-01-16
Category : Mathematics
ISBN : 0471635197

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Introduction to Modern Set Theory by Judith Roitman Pdf

This is modern set theory from the ground up--from partial orderings and well-ordered sets to models, infinite cobinatorics and large cardinals. The approach is unique, providing rigorous treatment of basic set-theoretic methods, while integrating advanced material such as independence results, throughout. The presentation incorporates much interesting historical material and no background in mathematical logic is assumed. Treatment is self-contained, featuring theorem proofs supported by diagrams, examples and exercises. Includes applications of set theory to other branches of mathematics.

Author : Theodore A. Sundstrom
Publisher : Prentice Hall
Page : 0 pages
File Size : 52,9 Mb
Release : 2007
Category : Logic, Symbolic and mathematical
ISBN : 0131877186

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Mathematical Reasoning by Theodore A. Sundstrom Pdf

Focusing on the formal development of mathematics, this book shows readers how to read, understand, write, and construct mathematical proofs.Uses elementary number theory and congruence arithmetic throughout. Focuses on writing in mathematics. Reviews prior mathematical work with “Preview Activities” at the start of each section. Includes “Activities” throughout that relate to the material contained in each section. Focuses on Congruence Notation and Elementary Number Theorythroughout.For professionals in the sciences or engineering who need to brush up on their advanced mathematics skills. Mathematical Reasoning: Writing and Proof, 2/E Theodore Sundstrom