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Metamathematics of First-Order Arithmetic

$155.00 (C)

Part of Perspectives in Logic

  • Authors:
  • Petr Hájek, Academy of Sciences of the Czech Republic, Prague
  • Pavel Pudlák, Academy of Sciences of the Czech Republic, Prague
  • Date Published: March 2017
  • availability: Available
  • format: Hardback
  • isbn: 9781107168411

$ 155.00 (C)
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About the Authors
  • Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the third publication in the Perspectives in Logic series, is a much-needed monograph on the metamathematics of first-order arithmetic. The authors pay particular attention to subsystems (fragments) of Peano arithmetic and give the reader a deeper understanding of the role of the axiom schema of induction and of the phenomenon of incompleteness. The reader is only assumed to know the basics of mathematical logic, which are reviewed in the preliminaries. Part I develops parts of mathematics and logic in various fragments. Part II is devoted to incompleteness. Finally, Part III studies systems that have the induction schema restricted to bounded formulas (bounded arithmetic).

    • Presents a much-needed review of the metamathematics of first-order arithmetic
    • Allows readers to better understand the role of the axiom schema of induction and the phenomenon of incompleteness
    • Assumes only a basic knowledge of mathematical logic
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    Reviews & endorsements

    '… a very important contribution to the logical literature. It gives a survey of an incredible number of results and methods in the foundations of arithmetic, presented in a clear and systematic way. It will certainly be highly appreciated by specialists working in the field.' Roman Murawski, Mathematical Reviews

    '… really a highly interesting book - a survey of a large amount of results presented in a systematic and clear way. It will serve as a source of information for those who want to learn metamathematics of first-order arithmetic as well as a reference book for people working in this field.' Zentralblatt fύr Mathematϊk und ihre Grenzgebiete

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    Product details

    • Date Published: March 2017
    • format: Hardback
    • isbn: 9781107168411
    • dimensions: 240 x 162 x 36 mm
    • weight: 0.91kg
    • contains: 2 b/w illus.
    • availability: Available
  • Table of Contents

    Introduction
    Preliminaries
    Part I:
    1. Arithmetic as number theory, set theory and logic
    2. Fragments and combinatorics
    Part II:
    3. Self-reference
    4. Models of fragments of arithmetic
    Part III:
    5. Bounded arithmetic
    Bibliographical remarks and further reading
    Bibliography
    Index of terms
    Index of symbols.

  • Authors

    Petr Hájek, Academy of Sciences of the Czech Republic, Prague
    Petr Hájek works in the Institute of Computer Science at the Academy of Sciences of the Czech Republic, Prague.

    Pavel Pudlák, Academy of Sciences of the Czech Republic, Prague
    Pavel Pudlák works in the Mathematical Institute at the Academy of Sciences of the Czech Republic, Prague.

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