Combinatorial Set Theory

With a Gentle Introduction to Forcing

  • Lorenz J. Halbeisen

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Preliminary

    1. Front Matter
      Pages 1-1
    2. Lorenz J. Halbeisen
      Pages 3-9
    3. Lorenz J. Halbeisen
      Pages 11-29
    4. Lorenz J. Halbeisen
      Pages 31-83
  3. Topics in Combinatorial Set Theory

    1. Front Matter
      Pages 85-85
    2. Lorenz J. Halbeisen
      Pages 87-102
    3. Lorenz J. Halbeisen
      Pages 103-134
    4. Lorenz J. Halbeisen
      Pages 135-175
    5. Lorenz J. Halbeisen
      Pages 177-190
    6. Lorenz J. Halbeisen
      Pages 191-219
    7. Lorenz J. Halbeisen
      Pages 221-243
    8. Lorenz J. Halbeisen
      Pages 245-257
    9. Lorenz J. Halbeisen
      Pages 259-292
    10. Lorenz J. Halbeisen
      Pages 293-315
  4. Part III

    1. Front Matter
      Pages 317-317
    2. Lorenz J. Halbeisen
      Pages 319-321
    3. Lorenz J. Halbeisen
      Pages 323-338
    4. Lorenz J. Halbeisen
      Pages 339-368
    5. Lorenz J. Halbeisen
      Pages 369-381

About this book


This book, now in a thoroughly revised second edition, provides a comprehensive and accessible introduction to modern set theory.

Following an overview of basic notions in combinatorics and first-order logic, the author outlines the main topics of classical set theory in the second part, including Ramsey theory and the axiom of choice. The revised edition contains new permutation models and recent results in set theory without the axiom of choice. The third part explains the sophisticated technique of forcing in great detail, now including a separate chapter on Suslin’s problem. The technique is used to show that certain statements are neither provable nor disprovable from the axioms of set theory. In the final part, some topics of classical set theory are revisited and further developed in light of forcing, with new chapters on Sacks Forcing and Shelah’s astonishing construction of a model with finitely many Ramsey ultrafilters.

Written for graduate students in axiomatic set theory, Combinatorial Set Theory will appeal to all researchers interested in the foundations of mathematics. With extensive reference lists and historical remarks at the end of each chapter, this book is suitable for self-study.


axiom of choice Banach-Tarski paradox cardinal characteristics combinatorics of forcing forcing constructions forcing technique infinite combinatorics Martin's axiom permutation models Ramsey theory Ramsey ultrafilters set theory Suslin's problem MSC (2010): 03E35, 03E17, 03E25, 05D10, 03E30, 03E50, 03E05

Authors and affiliations

  • Lorenz J. Halbeisen
    • 1
  1. 1.Department of MathematicsETH Zurich ZurichSwitzerland

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-60230-1
  • Online ISBN 978-3-319-60231-8
  • Series Print ISSN 1439-7382
  • Series Online ISSN 2196-9922
  • About this book