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Discovering Modern Set Theory. I: The Basics
Winfried Just, Ohio University, Athens, OH, and Martin Weese, Humboldt University, Berlin, Germany
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Graduate Studies in Mathematics
1996; 210 pp; hardcover
Volume: 8
Reprint/Revision History:
reprinted with corrections 1998
ISBN-10: 0-8218-0266-6
ISBN-13: 978-0-8218-0266-3
List Price: US$45
Member Price: US$36
Order Code: GSM/8
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See also:

Descriptive Set Theory: Second Edition - Yiannis N Moschovakis

This book is an introduction to set theory for beginning graduate students who want to get a sound grounding in those aspects of set theory used extensively throughout other areas of mathematics. Topics covered include formal languages and models, the power and limitation of the Axiomatic Method, the Axiom of Choice, including the fascinating Banach-Tarski Paradox, applications of Zorn's Lemma, ordinal arithmetic, including transfinite induction, and cardinal arithmetic. The style of writing, more a dialogue with the reader than that of the Master indoctrinating the pupil, makes this also very suitable for self-study.

Readership

Graduate students and mathematicians interested in set-theoretical techniques.

Reviews

"These books aim to support first courses in rigorous set theory ... are thoroughly competent: well-organized, scrupulous in pointing out both mathematical and philosophical difficulties, carefully graded from relatively straightforward beginnings to demanding conclusions. The more interesting, and more demanding, approach is that of Just and Weese. These books are for those who not only want to learn mathematics, but want to think about mathematics."

-- Bulletin of the London Mathematical Society

"Well written and userfriendly."

-- Zentralblatt MATH

"Serious graduate students ... would profit from reading the book for the mathematical maturity they would gain in the process. The conversational, almost Socratic, style of exposition is well suited to giving students some insight into the process of doing mathematics as well as to the importance of asking the right questions ... Just and Weese's text would be ideally suited for ... students who are serious about studying set theory."

-- Journal of Symbolic Logic

"The careful exposition, written in a lively and very readable style which addresses the reader rather directly, provides (by explanations, comments, and remarks) much information and motivation. Recommended."

-- Monatshefte für Mathematik

Table of Contents

  • Introduction
  • Pairs, relations, and functions
  • Partial order relations
  • Cardinality
  • Induction
  • Formal languages and models
  • Power and limitations of the axiomatic method
  • The axioms
  • Classes
  • Versions of the axiom of choice
  • The ordinals
  • The cardinals
  • Pictures of the universe
  • Subject index
  • Index of notation
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