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1 Burnside Mathematics- Set Theory

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Basic Set Theory

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Synopses & Reviews

Publisher Comments:

An advanced-level treatment of the basics of set theory, this text offers students a firm foundation, stopping just short of the areas employing model-theoretic methods. Geared toward upper-level undergraduate and graduate students, it consists of two parts: the first covers pure set theory, including the basic motions, order and well-foundedness, cardinal numbers, the ordinals, and the axiom of choice and some of it consequences; the second deals with applications and advanced topics such as point set topology, real spaces, Boolean algebras, and infinite combinatorics and large cardinals. An appendix comprises useful information on eliminability and conservation theorems, and numerous exercises help students test their grasp of each topic. 1979 edition. 20 figures.

Book News Annotation:

This advanced mathematics textbook introduces the theorems and proofs of cardinal numbers, the ordinals, the axiom of choice, the space of real numbers, Boolean algebras, trees, and partitions. Originally published by Springer Verlag in 1979, this reprint adds an appendix of corrections.
Annotation c. Book News, Inc., Portland, OR (booknews.com)

Synopsis:

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.

Table of Contents

Part A. Pure Set Theory

and#160; Chapter I. The Basic Notions

and#160;and#160;and#160; 1. The Basic Language of Set Theory

and#160;and#160;and#160; 2. The Axioms of Extensionality and Comprehension

and#160;and#160;and#160; 3. Classes, Why and How

and#160;and#160;and#160; 4. Classes, the formal Introduction

and#160;and#160;and#160; 5. The Axioms of Set Theory

and#160;and#160;and#160; 6. Relations and functions

and#160; Chapter II. Order and Well-Foundedness

and#160;and#160;and#160; 1. Order

and#160;and#160;and#160; 2. Well-Order

and#160;and#160;and#160; 3. Ordinals

and#160;and#160;and#160; 4. Natural Numbers and finite Sequences

and#160;and#160;and#160; 5. Well-Founded Relations

and#160;and#160;and#160; 6. Well-Founded Sets

and#160;and#160;and#160; 7. The Axiom of Foundation

and#160; Chapter III. Cardinal Numbers

and#160;and#160;and#160; 1. Finite Sets

and#160;and#160;and#160; 2. The Partial Order of the Cardinals

and#160;and#160;and#160; 3. The Finite Arithmetic of the Cardinals

and#160;and#160;and#160; 4. The Infinite Arithmetic of the Well Orderd Cardinals

and#160; Chapter IV. The Ordinals

and#160;and#160;and#160; 1. Ordinal Addition and Multiplication

and#160;and#160;and#160; 2. Ordinal Exponentiation

and#160;and#160;and#160; 3. Cofinality and Regular Ordinals

and#160;and#160;and#160; 4. Closed Unbounded Classes and Stationery Classes

and#160; Chapter V. The Axiom of Choice and Some of Its Consequences

and#160;and#160;and#160; 1. The Axiom of Choice and Equivalent Statements

and#160;and#160;and#160; 2. Some Weaker Versions of the Axiom of Choice

and#160;and#160;and#160; 3. Definable Sets

and#160;and#160;and#160; 4. Set Theory with Global Choice

and#160;and#160;and#160; 5. Cardinal Exponentiation

Part B. Applications and Advanced Topics

and#160; Chapter VI. A Review of Point Set Topology

and#160;and#160;and#160; 1. Basic concepts

and#160;and#160;and#160; 2. Useful Properties and Operations

and#160;and#160;and#160; 3. Category, Baire and Borel Sets

and#160; Chapter VII. The Real Spaces

and#160;and#160;and#160; 1. The Real Numbers

and#160;and#160;and#160; 2. The Separable Complete Metric Spaces

and#160;and#160;and#160; 3. The Close Relationship Between the Real Numbers, the Cantor Space and the Baire Space

and#160; Chapter VIII. Boolean Algebras

and#160;and#160;and#160; 1. The Basic Theory

and#160;and#160;and#160; 2. Prime Ideals and Representation

and#160;and#160;and#160; 3. Complete Boolean Algebras

and#160;and#160;and#160; 4. Martin's Axiom

and#160; Chapter IX. Infinite Combinatorics and Large Cardinals

and#160;and#160;and#160; 1. The Axiom of Constructibility

and#160;and#160;and#160; 2. Trees

and#160;and#160;and#160; 3. Partition Properties

and#160;and#160;and#160; 4. Measurable Cardinals

Appendix X. The Eliminability and Conservation Theorems

and#160; Bibliography; Additional Bibliography; Index of Notation; Index

Appendix Corrections and Additions

Product Details

ISBN:
9780486420790
Author:
Levy, Azriel
Publisher:
Dover Publications
Author:
Mathematics
Location:
Mineola, N.Y.
Subject:
Set Theory
Subject:
General Mathematics
Subject:
Mathematics : Set Theory
Copyright:
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Series Volume:
1083
Publication Date:
20020831
Binding:
TRADE PAPER
Language:
English
Illustrations:
20 Figures
Pages:
414
Dimensions:
9.25 x 6.13 in 1.2 lb

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Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Set Theory

Basic Set Theory Sale Trade Paper
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Product details 414 pages Dover Publications - English 9780486420790 Reviews:
"Synopsis" by ,
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.
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