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Discovering Modern Set Theory. I: The Basics
 
Winfried Just Ohio University, Athens, OH
Martin Weese Humboldt University, Berlin, Germany
Discovering Modern Set Theory. I: The Basics
Hardcover ISBN:  978-0-8218-0266-3
Product Code:  GSM/8
List Price: $99.00
MAA Member Price: $89.10
AMS Member Price: $79.20
eBook ISBN:  978-1-4704-2068-0
Product Code:  GSM/8.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Hardcover ISBN:  978-0-8218-0266-3
eBook: ISBN:  978-1-4704-2068-0
Product Code:  GSM/8.B
List Price: $184.00 $141.50
MAA Member Price: $165.60 $127.35
AMS Member Price: $147.20 $113.20
Discovering Modern Set Theory. I: The Basics
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Discovering Modern Set Theory. I: The Basics
Winfried Just Ohio University, Athens, OH
Martin Weese Humboldt University, Berlin, Germany
Hardcover ISBN:  978-0-8218-0266-3
Product Code:  GSM/8
List Price: $99.00
MAA Member Price: $89.10
AMS Member Price: $79.20
eBook ISBN:  978-1-4704-2068-0
Product Code:  GSM/8.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Hardcover ISBN:  978-0-8218-0266-3
eBook ISBN:  978-1-4704-2068-0
Product Code:  GSM/8.B
List Price: $184.00 $141.50
MAA Member Price: $165.60 $127.35
AMS Member Price: $147.20 $113.20
  • Book Details
     
     
    Graduate Studies in Mathematics
    Volume: 81996; 210 pp
    MSC: Primary 03;

    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.

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • Part 1: Not entirely naive set theory
    • Chapter 1. Pairs, relations, and functions
    • Chapter 2. Partial order relations
    • Chapter 3. Cardinality
    • Chapter 4. Induction
    • Part 2: An axiomatic foundation of set theory
    • Chapter 5. Formal languages and models
    • Chapter 6. Power and limitations of the axiomatic method
    • Chapter 7. The axioms
    • Chapter 8. Classes
    • Chapter 9. Versions of the Axiom of Choice
    • Chapter 10. The ordinals
    • Chapter 11. The Cardinals
    • Chapter 12. Pictures of the universe
  • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 81996; 210 pp
MSC: Primary 03;

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.

  • Chapters
  • Introduction
  • Part 1: Not entirely naive set theory
  • Chapter 1. Pairs, relations, and functions
  • Chapter 2. Partial order relations
  • Chapter 3. Cardinality
  • Chapter 4. Induction
  • Part 2: An axiomatic foundation of set theory
  • Chapter 5. Formal languages and models
  • Chapter 6. Power and limitations of the axiomatic method
  • Chapter 7. The axioms
  • Chapter 8. Classes
  • Chapter 9. Versions of the Axiom of Choice
  • Chapter 10. The ordinals
  • Chapter 11. The Cardinals
  • Chapter 12. Pictures of the universe
  • 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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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