BN.com Gift Guide

Set Theory

Hardcover (Print)
Used and New from Other Sellers
Used and New from Other Sellers
from $78.00
Usually ships in 1-2 business days
(Save 57%)
Other sellers (Hardcover)
  • All (5) from $78.00   
  • New (2) from $170.39   
  • Used (3) from $78.00   

Overview

This is a classic introduction to set theory, suitable for students with no previous knowledge of the subject. Providing complete, up-to-date coverage, the book is based in large part on courses given over many years by Professor Hajnal. The first part introduces all the standard notions of the subject; the second part concentrates on combinatorial set theory. Exercises are included throughout and a new section of hints has been added to assist the reader.

Read More Show Less

Editorial Reviews

From the Publisher
"The great number of exercises and problems (some of them with hints for solution) makes this book a valuable text for mathematics majors and also for an undergraduate course in mathematical logic." Monatshefte fur Mathematik
Read More Show Less

Product Details

Table of Contents

Preface
Pt. I Introduction to set theory 1
1 Notation, conventions 5
2 Definition of equivalence. The concept of cardinality. The Axiom of Choice 11
3 Countable cardinal, continuum cardinal 15
4 Comparison of cardinals 21
5 Operations with sets and cardinals 28
6 Examples 36
7 Ordered sets. Order types. Ordinals 41
8 Properties of wellordered sets. Good sets. The ordinal operation 54
9 Transfinite induction and recursion. Some consequences of the Axiom of Choice, the Wellordering Theorem 66
10 Definition of the cardinality operation. Properties of cardinalities. The cofinality operation 77
11 Properties of the power operation 93
App An axiomatic development of set theory 107
A1 The Zermelo-Fraenkel axiom system of set theory 111
A2 Definition of concepts; extension of the language 114
A3 A sketch of the development. Metatheorems 117
A4 A sketch of the development. Definitions of simple operations and properties (continued) 122
A5 A sketch of the development. Basic theorems, the introduction of [omega] and R (continued) 124
A6 The ZFC axiom system. A weakening of the Axiom of Choice. Remarks on the theorems of Sections 2-7 128
A7 The role of the Axiom of Regularity 130
A8 Proofs of relative consistency. The method of interpretation 133
A9 Proofs of relative consistency. The method of models 138
Pt. II Topics in combinatorial set theory 143
12 Stationary sets 145
13 [Delta]-systems 159
14 Ramsey's Theorem and its generalizations. Partition calculus 164
15 Inaccessible cardinals. Mahlo cardinals 184
16 Measurable cardinals 190
17 Real-valued measurable cardinals, saturated ideals 203
18 Weakly compact and Ramsey cardinals 216
19 Set mappings 228
20 The square-bracket symbol. Strengthenings of the Ramsey counterexamples 234
21 Properties of the power operation. Results on the singular cardinal problem 243
22 Powers of singular cardinals. Shelah's Theorem 259
Bibliography 295
List of symbols 297
Name index 301
Subject index 303
Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star

(0)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation

Reminder:

  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

 
Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)