Set Theory

Exploring Independence and Truth

  • Ralf Schindler

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-x
  2. Ralf Schindler
    Pages 1-8
  3. Ralf Schindler
    Pages 9-21
  4. Ralf Schindler
    Pages 23-31
  5. Ralf Schindler
    Pages 33-65
  6. Ralf Schindler
    Pages 67-91
  7. Ralf Schindler
    Pages 93-126
  8. Ralf Schindler
    Pages 127-146
  9. Ralf Schindler
    Pages 147-164
  10. Ralf Schindler
    Pages 165-182
  11. Ralf Schindler
    Pages 183-233
  12. Ralf Schindler
    Pages 235-278
  13. Ralf Schindler
    Pages 279-302
  14. Ralf Schindler
    Pages 303-323
  15. Back Matter
    Pages 325-332

About this book


This textbook gives an introduction to axiomatic set theory and examines the prominent questions that are relevant in current research in a manner that is accessible to students. Its main theme is the interplay of large cardinals, inner models, forcing, and descriptive set theory.
The following topics are covered:
• Forcing and constructability
• The Solovay-Shelah Theorem i.e. the equiconsistency of ‘every set of reals is Lebesgue measurable’ with one inaccessible cardinal
• Fine structure theory and a modern approach to sharps
• Jensen’s Covering Lemma
• The equivalence of analytic determinacy with sharps
• The theory of extenders and iteration trees
• A proof of projective determinacy from Woodin cardinals.
Set Theory requires only a basic knowledge of mathematical logic and will be suitable for advanced students and researchers.


Constructibility Extenders Fine Structure Theory Forcing Iteration Trees Jensen’s Covering Lemma Large Cardinals Solovay’s Model The Martin-Harrington Theorem The Martin-Steel Theorem The Solovay-Shelah Theorem

Authors and affiliations

  • Ralf Schindler
    • 1
  1. 1.Institut für Mathematische Logik und GruUniversität MünsterMünsterGermany

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-06724-7
  • Online ISBN 978-3-319-06725-4
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site