© 2003

The Higher Infinite

Large Cardinals in Set Theory from Their Beginnings


Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages I-XXII
  2. Pages 1-14
  3. Pages 15-67
  4. Pages 69-111
  5. Pages 209-295
  6. Pages 297-365
  7. Pages 367-471
  8. Back Matter
    Pages 472-538

About this book


The theory of large cardinals is currently a broad mainstream of modern set theory, the main area of investigation for the analysis of the relative consistency of mathematical propositions and possible new axioms for mathematics. The first of a projected multi-volume series, this book provides a comprehensive account of the theory of large cardinals from its beginnings and some of the direct outgrowths leading to the frontiers of contempory research. A "genetic" approach is taken, presenting the subject in the context of its historical development. With hindsight the consequential avenues are pursued and the most elegant or accessible expositions given. With open questions and speculations provided throughout the reader should not only come to appreciate the scope and coherence of the overall enterpreise but also become prepared to pursue research in several specific areas by studying the relevant sections.


cardinals infinitary combinatorics large cardinals new axioms for set theory relative consistency results set theory

Authors and affiliations

  1. 1.Department of MathematicsBoston UniversityBostonUSA

Bibliographic information

  • Book Title The Higher Infinite
  • Book Subtitle Large Cardinals in Set Theory from Their Beginnings
  • Authors Akihiro Kanamori
  • Series Title Springer Monographs in Mathematics
  • DOI
  • Copyright Information Springer Berlin Heidelberg 2003
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-3-540-00384-7
  • Softcover ISBN 978-3-540-88866-6
  • eBook ISBN 978-3-540-88867-3
  • Series ISSN 1439-7382
  • Edition Number 2
  • Number of Pages XXII, 538
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Additional Information Originally published in the series: Perpectives Mathematical Logic
  • Topics Mathematical Logic and Foundations
  • Buy this book on publisher's site