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Introduction to Set Theory, Third Edition, Revised and Expanded : Pure and Applied Mathematics - Karel Hrbacek

Introduction to Set Theory, Third Edition, Revised and Expanded

Pure and Applied Mathematics

Hardcover

Published: 22nd June 1999
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Thoroughly revised, updated, expanded, and reorganized to serve as a primary text for mathematics courses, Introduction to Set Theory, Third Edition covers the basics: relations, functions, orderings, finite, countable, and uncountable sets, and cardinal and ordinal numbers. It also provides five additional self-contained chapters, consolidates the material on real numbers into a single updated chapter affording flexibility in course design, supplies end-of-section problems, with hints, of varying degrees of difficulty, includes new material on normal forms and Goodstein sequences, and adds important recent ideas including filters, ultrafilters, closed unbounded and stationary sets, and partitions.

"The book remains an excellent text for a senior undergraduate or first-year graduate level course. There is sufficient material for instructors of widely differing views to assemble one-semester courses. . ..the chapter on the axiom of choice is particularly strong." ---Mathematical Reviews ." . .a fine text. . ..The proofs are both elegant and readable." ---American Mathematical Monthly ." . .offers many benefits including. . .interesting applications of abstract set theory to real analysis. . .enriching standard classroom material." ---L'Enseignement mathematique ." . .an excellent and much needed book. . .Especially valuable are a number of remarks sprinkled throughout the text which afford a glimpse of further developments." ---The Mathematical Intelligencer "The authors show that set theory is powerful enough to serve as an underlying framework for mathematics by using it to develop the beginnings of the theory of natural, rational, and real numbers." ---Quarterly Review of Applied Mathematics ." . .In the third edition, Chapter 11 has been expanded, and four new chapters have been added." ---Mathematical Reviews

Sets
relations, functions and orderings
natural numbers
finite, countable and uncountable sets
cardinal numbers
ordinal numbers
alephs
the axiom of choice
arithmetic of cardinal numbers
sets of real numbers
filters and ultrafilters
combinatorial set theory
large cardinals
the axiom of foundation
the axiomatic set theory
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780824779153
ISBN-10: 0824779150
Series: Pure and Applied Mathematics
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 310
Published: 22nd June 1999
Publisher: Taylor & Francis Inc
Country of Publication: US
Dimensions (cm): 24.13 x 16.51  x 1.91
Weight (kg): 0.49
Edition Number: 3
Edition Type: New edition