Lecture Notes in Mathematics

Axiom of Choice

Authors: Herrlich, Horst

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About this book

AC, the axiom of choice, because of its non-constructive character, is the most controversial mathematical axiom, shunned by some, used indiscriminately by others. This treatise shows paradigmatically that:

  1. Disasters happen without AC: Many fundamental mathematical results fail (being equivalent in ZF to AC or to some weak form of AC).
  2. Disasters happen with AC: Many undesirable mathematical monsters are being created (e.g., non measurable sets and undeterminate games).
  3. Some beautiful mathematical theorems hold only if AC is replaced by some alternative axiom, contradicting AC (e.g., by AD, the axiom of determinateness).

Illuminating examples are drawn from diverse areas of mathematics, particularly from general topology, but also from algebra, order theory, elementary analysis, measure theory, game theory, and graph theory.

Reviews

From the reviews:

"The book is an excellent introduction to the Axiom of Choice, its consequences and even its possible replacements. Although the author claims not to have written a textbook, compendium or history, the book might be used as any of these three. … there are many diagrams throughout the text and in the appendix detailing the relationships between the Axiom of Choice and its consequences. It certainly fulfills its stated purpose of whetting the reader’s appetite for studying the ZF universe." (Paul E. Howard, Mathematical Reviews, Issue 2007 f)


Table of contents (7 chapters)

Table of contents (7 chapters)

Buy this book

eBook $44.99
price for USA in USD
  • ISBN 978-3-540-34268-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA in USD
  • ISBN 978-3-540-30989-5
  • 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
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Bibliographic Information

Bibliographic Information
Book Title
Axiom of Choice
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1876
Copyright
2006
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-34268-7
DOI
10.1007/11601562
Softcover ISBN
978-3-540-30989-5
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XIV, 198
Number of Illustrations
1 b/w illustrations
Topics