A Book of Set Theory

2014-06-01
 |  Mathematics
A Book of Set Theory

Author: Charles C Pinter

Publisher: Courier Corporation

ISBN: 9780486795492

Category: Mathematics

Page: 256

View: 419

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Accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. Topics include classes and sets, functions, natural and cardinal numbers, arithmetic of ordinal numbers, and more. 1971 edition with new material by author.

Set Theory

2007-05-23
 |  Mathematics
Set Theory

Author: Thomas Jech

Publisher: Springer Science & Business Media

ISBN: 9783540447610

Category: Mathematics

Page: 772

View: 835

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This monograph covers the recent major advances in various areas of set theory. From the reviews: "One of the classical textbooks and reference books in set theory....The present ‘Third Millennium’ edition...is a whole new book. In three parts the author offers us what in his view every young set theorist should learn and master....This well-written book promises to influence the next generation of set theorists, much as its predecessor has done." --MATHEMATICAL REVIEWS

Basic Set Theory

2012-06-11
 |  Mathematics
Basic Set Theory

Author: Azriel Levy

Publisher: Courier Corporation

ISBN: 9780486150734

Category: Mathematics

Page: 416

View: 803

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The first part of this advanced-level text covers pure set theory, and the second deals with applications and advanced topics (point set topology, real spaces, Boolean algebras, infinite combinatorics and large cardinals). 1979 edition.

Intermediate Set Theory

1996-09-11
 |  Mathematics
Intermediate Set Theory

Author: F. R. Drake

Publisher: John Wiley & Sons Incorporated

ISBN: UCSD:31822023645690

Category: Mathematics

Page: 256

View: 438

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The authors cover first order logic and the main topics of set theory in a clear mathematical style with sensible philosophical discussion. The emphasis is on presenting the use of set theory in various areas of mathematics, with particular attention paid to introducing axiomatic set theory, showing how the axioms are needed in mathematical practice and how they arise. Other areas introduced include the axiom of choice, filters and ideals. Exercises are provided which are suitable for both beginning students and degree-level students.

Concise Introduction to Logic and Set Theory

2021-10-14
 |  Technology & Engineering
Concise Introduction to Logic and Set Theory

Author: Iqbal H. Jebril

Publisher: CRC Press

ISBN: 9780429663260

Category: Technology & Engineering

Page: 168

View: 249

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This book deals with two important branches of mathematics, namely, logic and set theory. Logic and set theory are closely related and play very crucial roles in the foundation of mathematics, and together produce several results in all of mathematics. The topics of logic and set theory are required in many areas of physical sciences, engineering, and technology. The book offers solved examples and exercises, and provides reasonable details to each topic discussed, for easy understanding. The book is designed for readers from various disciplines where mathematical logic and set theory play a crucial role. The book will be of interested to students and instructors in engineering, mathematics, computer science, and technology.

Introduction to Set Theory and Topology

2014-07-10
 |  Mathematics
Introduction to Set Theory and Topology

Author: Kazimierz Kuratowski

Publisher: Elsevier

ISBN: 9781483151632

Category: Mathematics

Page: 352

View: 448

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Introduction to Set Theory and Topology describes the fundamental concepts of set theory and topology as well as its applicability to analysis, geometry, and other branches of mathematics, including algebra and probability theory. Concepts such as inverse limit, lattice, ideal, filter, commutative diagram, quotient-spaces, completely regular spaces, quasicomponents, and cartesian products of topological spaces are considered. This volume consists of 21 chapters organized into two sections and begins with an introduction to set theory, with emphasis on the propositional calculus and its application to propositions each having one of two logical values, 0 and 1. Operations on sets which are analogous to arithmetic operations are also discussed. The chapters that follow focus on the mapping concept, the power of a set, operations on cardinal numbers, order relations, and well ordering. The section on topology explores metric and topological spaces, continuous mappings, cartesian products, and other spaces such as spaces with a countable base, complete spaces, compact spaces, and connected spaces. The concept of dimension, simplexes and their properties, and cuttings of the plane are also analyzed. This book is intended for students and teachers of mathematics.

Naive Set Theory

2013-11-27
 |  Mathematics
Naive Set Theory

Author: P. R. Halmos

Publisher: Springer Science & Business Media

ISBN: 9781475716450

Category: Mathematics

Page: 104

View: 664

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Every mathematician agrees that every mathematician must know some set theory; the disagreement begins in trying to decide how much is some. This book contains my answer to that question. The purpose of the book is to tell the beginning student of advanced mathematics the basic set theoretic facts of life, and to do so with the minimum of philosophical discourse and logical formalism. The point of view throughout is that of a prospective mathematician anxious to study groups, or integrals, or manifolds. From this point of view the concepts and methods of this book are merely some of the standard mathematical tools; the expert specialist will find nothing new here. Scholarly bibliographical credits and references are out of place in a purely expository book such as this one. The student who gets interested in set theory for its own sake should know, however, that there is much more to the subject than there is in this book. One of the most beautiful sources of set-theoretic wisdom is still Hausdorff's Set theory. A recent and highly readable addition to the literature, with an extensive and up-to-date bibliography, is Axiomatic set theory by Suppes.

Mengenlehre und ihre Logik

1973-01-01
 |  Mathematics
Mengenlehre und ihre Logik

Author: Willard van Orman Quine

Publisher: Vieweg+Teubner Verlag

ISBN: 3528082941

Category: Mathematics

Page: 0

View: 818

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einem solchen Panoramablick beginnen, denn der Leser wird zu Anfang weder den Stoff zu schatzen wissen, den die verschiedenen Systeme organisieren wollen, noch solehe Oberlegungen, die dem einen System in irgendeiner Hinsicht vor einem anderen den Vorzug geben. Es ist besser, zu Anfang den Leser mit einem vorlaufigen inforrnellen Oberblick tiber den Gegenstand zu orientieren. Hier zeigen sich aber schon wieder Schwierigkeiten. Wenn soleh ein Oberblick tiber Trivialitaten hinausgehen solI, muB er auch eine ernstzunehmende und spitzfindige Argumentation zu Hilfe nehmen, die aber leicht in Antinomien einmtinden und sich somit selbst in Millkredit bringen kann, wenn man sie nicht auf eine von zwei moglichen Weisen vor diesen abbiegen laBt: Man konn­ te letzten Endes doch den informellen Zugang zu Gunsten eines axiomatischen aufgeben, oder man konnte listigerweise die Aufmerksamkeit des Lesers von gefahrlichen Fragen ablenken, bis die inforrnelle Orientierung zu Ende gebracht ist. Der letztgenannte Aus­ weg erfordert ein artistisches Konnen einer Art, auf das ein akademischer Lehrer nur mit Verachtung blicken kann, und letztlich fOOrt er doch bei solehen Lesem zu nichts, die bei jemand anders von den Antinomien horen. Wenn sie einmal davon gehort haben, konnen sie sich nicht mehr der Disziplin komplizierter informeller Argumente in ab­ strakter Mengenlehre unterwerfen, denn sie wissen nicht mehr, welehe intuitiven Argu­ mente eigentlich zahlen. Es hat schlieBlich seine Grtinde, warum Mengentheoretiker sich zur axiomatischen Methode fltichten.

Problems in Set Theory, Mathematical Logic and the Theory of Algorithms

2003-03-31
 |  Mathematics
Problems in Set Theory, Mathematical Logic and the Theory of Algorithms

Author: Igor Lavrov

Publisher: Springer Science & Business Media

ISBN: 0306477122

Category: Mathematics

Page: 306

View: 286

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Problems in Set Theory, Mathematical Logic and the Theory of Algorithms by I. Lavrov & L. Maksimova is an English translation of the fourth edition of the most popular student problem book in mathematical logic in Russian. It covers major classical topics in proof theory and the semantics of propositional and predicate logic as well as set theory and computation theory. Each chapter begins with 1-2 pages of terminology and definitions that make the book self-contained. Solutions are provided. The book is likely to become an essential part of curricula in logic.

Introduction To Set Theory

2010
 |  Set theory
Introduction To Set Theory

Author: A. K. Sharma

Publisher: Discovery Publishing House

ISBN: 8171418775

Category: Set theory

Page: 130

View: 174

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This book Introduction to Set Theory is very important in the field of modern algebra. It is very important to study this book to study modern mathematics. This book contain preliminary Notation, Sets, Subsets, Mapping Function and Relation. This book is useful to the students of under graduate, post graduate students and the candidate appearing in various competitions like pre Engineering/I.A.S/ P.C.S. etc. Contents: Preliminary Notation, Relations, Product or Composite of Mapping, Mapping or Functions

Basic Set Theory

2002
 |  Mathematics
Basic Set Theory

Author: Azriel Levy

Publisher: Courier Dover Publications

ISBN: 0486420795

Category: Mathematics

Page: 398

View: 692

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Geared toward upper-level undergraduate and graduate students, this text consists of two parts: the first covers pure set theory, and the second deals with applications and advanced topics (point set topology, real spaces, Boolean algebras, infinite combinatorics and large cardinals). Useful appendix; numerous exercises. 1979 edition. Includes 20 figures.