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Metamathematics of First-Order Arithmetic

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    0501039 - ÚI 2020 GB eng B - Monography
    Hájek, Petr - Pudlák, Pavel
    Metamathematics of First-Order Arithmetic.
    Cambridge: Cambridge University Press, 2017. 474 s. Perspectives in Logic. ISBN 978-1-107-16841-1
    Institutional support: RVO:67985807 ; RVO:67985840
    Keywords : Computer Science * Logic * Categories and Sets * Programming Languages and Applied Logic * Mathematics
    OECD category: Pure mathematics; Pure mathematics (MU-W)

    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). © 1998 Springer-Verlag Berlin Heidelberg and © 2016 Association for Symbolic Logic under license to Cambridge University Press.
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