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  3. Metamathematics of First-Order Arithmetic
  • Cited by 18
      • Petr Hájek, Academy of Sciences of the Czech Republic, Prague, Pavel Pudlák, Academy of Sciences of the Czech Republic, Prague
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    • Publisher:
      Cambridge University Press
      Publication date:
      March 2017
      March 2017
      ISBN:
      9781316717271
      9781107168411
      DOI:
      https://doi.org/10.1017/9781316717271
      Dimensions:
      (234 x 156 mm)
      Weight & Pages:
      0.91kg, 476 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics, Logic, Categories and Sets, Computer Science, Programming Languages and Applied Logic
      Series:
      Perspectives in Logic (3)
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    • Selected: Digital
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    Subjects:
    Mathematics, Logic, Categories and Sets, Computer Science, Programming Languages and Applied Logic
    Series:
    Perspectives in Logic (3)
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    Book description

    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).

    Reviews

    ‘… 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 Source: 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.'

    Source: Zentralblatt fύr Mathematϊk und ihre Grenzgebiete

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