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The Logic of Infinity

£32.99

  • Date Published: July 2014
  • availability: Available
  • format: Paperback
  • isbn: 9781107678668

£ 32.99
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About the Authors
  • Few mathematical results capture the imagination like Georg Cantor's groundbreaking work on infinity in the late nineteenth century. This opened the door to an intricate axiomatic theory of sets which was born in the decades that followed. Written for the motivated novice, this book provides an overview of key ideas in set theory, bridging the gap between technical accounts of mathematical foundations and popular accounts of logic. Readers will learn of the formal construction of the classical number systems, from the natural numbers to the real numbers and beyond, and see how set theory has evolved to analyse such deep questions as the status of the continuum hypothesis and the axiom of choice. Remarks and digressions introduce the reader to some of the philosophical aspects of the subject and to adjacent mathematical topics. The rich, annotated bibliography encourages the dedicated reader to delve into what is now a vast literature.

    • Ideal for the novice, whether they are a student or a researcher in another area of mathematics
    • Author gives an overview of the subject, avoiding too many technicalities
    • Extensive bibliography gives readers from all backgrounds ideas for further study
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    Product details

    • Date Published: July 2014
    • format: Paperback
    • isbn: 9781107678668
    • length: 498 pages
    • dimensions: 246 x 170 x 28 mm
    • weight: 0.95kg
    • contains: 45 b/w illus.
    • availability: Available
  • Table of Contents

    Preface
    Synopsis
    1. Introduction
    2. Logical foundations
    3. Avoiding Russell's paradox
    4. Further axioms
    5. Relations and order
    6. Ordinal numbers and the axiom of infinity
    7. Infinite arithmetic
    8. Cardinal numbers
    9. The axiom of choice and the continuum hypothesis
    10. Models
    11. From Gödel to Cohen
    Appendix A. Peano arithmetic
    Appendix B. Zermelo–Fraenkel set theory
    Appendix C. Gödel's incompleteness theorems
    Bibliography
    Index.

  • Author

    Barnaby Sheppard
    Barnaby Sheppard is a freelance writer. He has previously held positions at Lancaster University, the University of Durham and University College Dublin.

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