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. Topics in Combinatorial Set Theory

    1. Front Matter
      Pages 7-7
    2. Lorenz J. Halbeisen
      Pages 1-6
  3. Topics in Combinatorial Set Theory

    1. Front Matter
      Pages 7-7
    2. Lorenz J. Halbeisen
      Pages 9-24
    3. Lorenz J. Halbeisen
      Pages 25-70
    4. Lorenz J. Halbeisen
      Pages 71-100
    5. Lorenz J. Halbeisen
      Pages 101-141
    6. Lorenz J. Halbeisen
      Pages 143-155
    7. Lorenz J. Halbeisen
      Pages 157-177
    8. Lorenz J. Halbeisen
      Pages 179-199
    9. Lorenz J. Halbeisen
      Pages 201-213
    10. Lorenz J. Halbeisen
      Pages 215-233
    11. Lorenz J. Halbeisen
      Pages 235-255
  4. From Martin’s Axiom to Cohen’s Forcing

    1. Front Matter
      Pages 257-257
    2. Lorenz J. Halbeisen
      Pages 259-261
    3. Lorenz J. Halbeisen
      Pages 263-272
    4. Lorenz J. Halbeisen
      Pages 273-293
    5. Lorenz J. Halbeisen
      Pages 295-303
    6. Lorenz J. Halbeisen
      Pages 305-310

About this book

Introduction

This book provides a self-contained introduction to modern set theory and also opens up some more advanced areas of current research in this field. The first part offers an overview of classical set theory wherein the focus lies on the axiom of choice and Ramsey theory. In the second part, the sophisticated technique of forcing, originally developed by Paul Cohen, is explained in great detail. With this technique, one can show that certain statements, like the continuum hypothesis, are neither provable nor disprovable from the axioms of set theory. In the last part, some topics of classical set theory are revisited and further developed in the light of forcing.

The notes at the end of each chapter put the results in a historical context, and the numerous related results and the extensive list of references lead the reader to the frontier of research.

This book will appeal to all mathematicians interested in the foundations of mathematics, but will be of particular use to graduates in this field.

Keywords

Axiom of Choice Cardinal Characteristics of the Continuum Combinatorics of Forcing Consistency and Independence Results Continuum Hypothesis Forcing Forcing Technique Infinite Combinatorics Ramsey Theory Set Theory

Authors and affiliations

  • Lorenz J. Halbeisen
    • 1
  1. 1.Institut für MathematikUniversität ZürichZürichSwitzerland

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4471-2173-2
  • Copyright Information Springer-Verlag London Limited 2012
  • Publisher Name Springer, London
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4471-2172-5
  • Online ISBN 978-1-4471-2173-2
  • Series Print ISSN 1439-7382
  • About this book