Springer Monographs in Mathematics

Combinatorial Set Theory

With a Gentle Introduction to Forcing

Authors: Halbeisen, Lorenz J.

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  • Provides a comprehensive introduction to the sophisticated technique of forcing
  • Complete proofs of famous results are given, for instance, Robinson’s construction of doubling the unit ball using just five pieces
  • Offers an extensive list of references, historical remarks and related results
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eBook 96,29 €
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  • ISBN 978-1-4471-2173-2
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Hardcover 124,79 €
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  • ISBN 978-1-4471-2172-5
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About this book

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.

Reviews

From the reviews:

“The text is very well organised; each chapter ends with useful notes containing much historical background and the source of the main results, together with reports on related results and the references. The beautifully written book is intended for students on graduate courses in axiomatic set theory, and it is also excellent as a text for self-study.” (Peter Shiu, The Mathematical Gazette, Vol. 98 (541), March, 2014)

“The book under review provides a thorough and nicely written account of combinatorial set theory and infinite Ramsey theory together with a treatment of the underlying set theoretical axioms as well as of sophisticated methods which are involved in proving independence results. … I can recommend this book to all graduate students, PostDocs, and researchers who are interested in set theoretical combinatorics … . also mathematicians from other areas who are interested in the foundational aspects of their subject will enjoy this book.” (Ralf Schindler, Jahresbericht der Deutschen Mathematiker-Vereinigung, Vol. 115, 2013)

“This book provides a self-contained introduction to axiomatic set theory with main focus on infinitary combinatorics and the forcing technique. It is intended as a textbook in courses as well as for self-study. … The author gives the historical background and the sources of the main results in the Notes of each chapter. He also gives hints for further studies in his sections ‘Related results’.” (Martin Weese, Zentralblatt MATH, Vol. 1237, 2012)


Table of contents (27 chapters)

Table of contents (27 chapters)

Buy this book

eBook 96,29 €
price for Spain (gross)
  • ISBN 978-1-4471-2173-2
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 124,79 €
price for Spain (gross)
  • ISBN 978-1-4471-2172-5
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Combinatorial Set Theory
Book Subtitle
With a Gentle Introduction to Forcing
Authors
Series Title
Springer Monographs in Mathematics
Copyright
2012
Publisher
Springer-Verlag London
Copyright Holder
Springer-Verlag London Limited
eBook ISBN
978-1-4471-2173-2
DOI
10.1007/978-1-4471-2173-2
Hardcover ISBN
978-1-4471-2172-5
Series ISSN
1439-7382
Edition Number
1
Number of Pages
XVI, 456
Topics