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    • Publisher:
      Cambridge University Press
      Publication date:
      05 January 2012
      15 December 2011
      ISBN:
      9781139031905
      9780521517690
      DOI:
      https://doi.org/10.1017/CBO9781139031905
      Dimensions:
      (234 x 156 mm)
      Weight & Pages:
      0.86kg, 480 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics, Logic, Categories and Sets, Computer Science, Programming Languages and Applied Logic
      Series:
      Perspectives in Logic
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    Subjects:
    Mathematics, Logic, Categories and Sets, Computer Science, Programming Languages and Applied Logic
    Series:
    Perspectives in Logic
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    Book description

    Driven by the question, 'What is the computational content of a (formal) proof?', this book studies fundamental interactions between proof theory and computability. It provides a unique self-contained text for advanced students and researchers in mathematical logic and computer science. Part I covers basic proof theory, computability and Gödel's theorems. Part II studies and classifies provable recursion in classical systems, from fragments of Peano arithmetic up to Π11–CA0. Ordinal analysis and the (Schwichtenberg–Wainer) subrecursive hierarchies play a central role and are used in proving the 'modified finite Ramsey' and 'extended Kruskal' independence results for PA and Π11–CA0. Part III develops the theoretical underpinnings of the first author's proof assistant MINLOG. Three chapters cover higher-type computability via information systems, a constructive theory TCF of computable functionals, realizability, Dialectica interpretation, computationally significant quantifiers and connectives and polytime complexity in a two-sorted, higher-type arithmetic with linear logic.

    Reviews

    "Written by two leading practitioners in the area of formal logic, the book provides a panoramic view of the topic. This reference volume is a must for the bookshelf of every practitioner of formal logic and computer science."
    Prahladavaradan Sampath, Computing Reviews

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