Problems and Theorems in Classical Set Theory

  • Péter Komjáth
  • Vilmos Totik

Part of the Problem Books in Mathematics book series (PBM)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Problems

    1. Front Matter
      Pages 1-1
    2. Pages 3-7
    3. Pages 9-12
    4. Pages 13-14
    5. Pages 15-18
    6. Pages 23-31
    7. Pages 33-36
    8. Pages 37-41
    9. Pages 43-50
    10. Pages 51-54
    11. Pages 63-64
    12. Pages 65-66
    13. Pages 67-69
    14. Pages 75-78
    15. Pages 79-80

About this book


This is the first comprehensive collection of problems in set theory. Most of classical set theory is covered, classical in the sense that independence methods are not used, but classical also in the sense that most results come from the period between 1920-1970. Many problems are also related to other fields of mathematics such as algebra, combinatorics, topology and real analysis.  The authors choose not to concentrate on the axiomatic framework, although some aspects are elaborated (axiom of foundation and the axiom of choice).  Rather than using drill exercises, most problems are challenging and require work, wit, and inspiration. The problems are organized in a way that earlier problems help in the solution of later ones. For many problems, the authors trace the origin and provide proper references at the end of the solution.

The book follows a tradition of Hungarian mathematics started with Pólya-Szegõ's problem book in analysis and continued with Lovász' problem book in combinatorics.   This is destined to become a classic, and will be an important resource for students and researchers.

Péter Komjáth is a professor of mathematics at the Eötvös Lóránd University, Budapest.  Vilmos Totik is a professor of mathematics at the University of South Florida, Tampa and University of Szeged.


Arithmetic Combinatorics Equivalence Lemma Partition cardinals graphs mapping set theory

Authors and affiliations

  • Péter Komjáth
    • 1
  • Vilmos Totik
    • 2
    • 3
  1. 1.Department of Computer ScienceEotvos Lorand University, BudapestBudapestHungary
  2. 2.Department of MathematicsUniversity of South FloridaTampaUSA
  3. 3.Bolyai InstituteUniversity of SzegedSzegedHungary

Bibliographic information

  • DOI
  • Copyright Information Springer Science+Business Media, LLC 2006
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-30293-5
  • Online ISBN 978-0-387-36219-9
  • Series Print ISSN 0941-3502
  • About this book