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  • Book
  • © 2003

The Higher Infinite

Large Cardinals in Set Theory from Their Beginnings

Authors:

  1. Akihiro Kanamori

    1. Department of Mathematics, Boston University, Boston, USA

    View author publications

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  • 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)

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Table of contents (7 chapters)

  1. Front Matter

    Pages I-XXII
    PDF

  2. Preliminaries

    Pages 1-14

  3. Beginnings

    Pages 15-67

  4. Partition Properties

    Pages 69-111

  6. Aspects of Measurability

    Pages 209-295

  7. Strong Hypotheses

    Pages 297-365

  8. Determinacy

    Pages 367-471

  9. Back Matter

    Pages 472-538
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About this book

The higher in?nite refers to the lofty reaches of the in?nite cardinalities of set t- ory as charted out by large cardinal hypotheses. These hypotheses posit cardinals that prescribe their own transcendence over smaller cardinals and provide a sup- structure for the analysis of strong propositions. As such they are the rightful heirs to the two main legacies of Georg Cantor, founder of set theory: the extension of number into the in?nite and the investigation of de?nable sets of reals. The investigation of large cardinal hypotheses is indeed a mainstream of modern set theory, and they have been found to play a crucial role in the study of de?nable sets of reals, in particular their Lebesgue measurability. Although formulated at various stages in the development of set theory and with different incentives, the hypotheses were found to form a linear hierarchy reaching up to an inconsistent extension of motivating concepts. All known set-theoretic propositions have been gauged in this hierarchy in terms of consistency strength, and the emerging str- ture of implications provides a remarkably rich, detailed and coherent picture of the strongest propositions of mathematics as embedded in set theory. The ?rst of a projected multi-volume series, this text provides a comp- hensive account of the theory of large cardinals from its beginnings through the developments of the early 1970’s and several of the direct outgrowths leading to the frontiers of current research.
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Keywords

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

  • Department of Mathematics, Boston University, Boston, USA

    Akihiro Kanamori

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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: 978-3-540-88866-6Published: 28 November 2008

  • eBook ISBN: 978-3-540-88867-3Published: 23 November 2008

  • 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

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Access via your institution

Buy it now

eBook USD 109.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 139.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

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