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Universitext

Set Theory

Exploring Independence and Truth

Authors: Schindler, Ralf

  • Provides a fairly self-contained introduction to set theory, in particular to the theory of inner models and forcing
  • Presents essential aspects of set theory which are required in understanding modern developments of descriptive inner model theory
  • Includes proofs of landmark results at the interface of the theory of large cardinals and descriptive set theory
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eBook $59.99
price for USA (gross)
  • ISBN 978-3-319-06725-4
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $79.99
price for USA
  • ISBN 978-3-319-06724-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
About this Textbook

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.

About the authors

Ralf Schindler teaches at Universität Münster and is an expert in the field of set theory.

Ralf Schindler works mostly in the area of descriptive inner model theory. His results are on the construction of inner models and core models, on coding over core models and on applications of inner model theory to descriptive set theory and combinatorics. He isolated the concept of a “remarkable” cardinal.

Reviews

“This text is, in its own way, a remarkable accomplishment. While a ‘Universitext’, it somehow manages to pursue a steady path of exposition from the beginnings in the seminal work of Cantor through to Jensen’s covering Lemma and the Martin-Steel Theorem on Projective Determinacy. … this text could well be considered an informative one even for the set theorist.” (A. Kanamori, Mathematical Reviews, June, 2015)

“The material is given in a form that is accessible to students. … The book contains many interesting problems which help the reader to follow and understand the presented material. This very carefully written book can be recommended to everyone seriously interested in modern set theory.” (Martin Weese, zbMATH, Vol. 1296, 2014)

Video

Table of contents (13 chapters)

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-3-319-06725-4
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $79.99
price for USA
  • ISBN 978-3-319-06724-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Set Theory
Book Subtitle
Exploring Independence and Truth
Authors
Series Title
Universitext
Copyright
2014
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
Distribution Rights
Distribution rights for India: Researchco Book Centre, New Delhi, India
eBook ISBN
978-3-319-06725-4
DOI
10.1007/978-3-319-06725-4
Softcover ISBN
978-3-319-06724-7
Series ISSN
0172-5939
Edition Number
1
Number of Pages
X, 332
Number of Illustrations and Tables
10 b/w illustrations
Topics