Skip to main content
  • Book
  • © 2003

The Higher Infinite

Large Cardinals in Set Theory from Their Beginnings

  • Has become a standard reference and guide in the set theory community

  • Includes supplementary material: sn.pub/extras

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

Buying options

eBook USD 119.00
Price excludes VAT (USA)
  • ISBN: 978-3-540-88867-3
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 159.99
Price excludes VAT (USA)

This is a preview of subscription content, access via your institution.

Table of contents (7 chapters)

  1. Front Matter

    Pages I-XXII
  2. Preliminaries

    Pages 1-14
  3. Beginnings

    Pages 15-67
  4. Partition Properties

    Pages 69-111
  5. Aspects of Measurability

    Pages 209-295
  6. Strong Hypotheses

    Pages 297-365
  7. Determinacy

    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.

Keywords

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

Authors and Affiliations

  • Department of Mathematics, Boston University, Boston, USA

    Akihiro Kanamori

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: https://doi.org/10.1007/978-3-540-88867-3

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2003

  • Softcover ISBN: 978-3-540-88866-6

  • eBook ISBN: 978-3-540-88867-3

  • Series ISSN: 1439-7382

  • Series E-ISSN: 2196-9922

  • Edition Number: 2

  • Number of Pages: XXII, 538

  • Additional Information: Originally published in the series: Perpectives Mathematical Logic

  • Topics: Mathematical Logic and Foundations, Topology

Buying options

eBook USD 119.00
Price excludes VAT (USA)
  • ISBN: 978-3-540-88867-3
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 159.99
Price excludes VAT (USA)