Proofs and Computations

di Helmut Schwichtenberg (Autore)

Stanley S. Wainer (Autore)

Cambridge University Press, 2011

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 Goedel's theorems. Part II studies and classifies provable recursion in classical systems, from fragments of Peano arithmetic up to 11-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 11-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.

• Autore: Helmut Schwichtenberg, Stanley S. Wainer
• Editore: Cambridge University Press
• Collana: Perspectives in Logic
• Anno: 2011
• Rilegatura: Hardback
• Pagine: 480 p.
• Dimensioni: 236 x 160 mm
• Peso: 860 gr.
• EAN: 9780521517690

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